
o 



A FRAGMENT. 



LONDON : 

CLAY, PRINTER, BREAD-STREET-HILL. 




THE NINTH 



/ 

BRIDGEWATER TREATISE. 



"We may thus, with the greatest propriety, deny to the mechanical philosophers 
and mathematicians of recent times any authority with regard to their views of 
the administration of the universe; we have no reason whatever to expect from 
their speculations any help, when we ascend to the first cause and supreme ruler 
of the universe. But we might perhaps go farther, and assert that they are in 
some respects less likely than men employed in other pursuits, to make any clear 
advance towards such a subject of speculation." — Bridgewater Treatise, l»i the 
Rev. Wm. Whewell, p. 334. 



A FRAGMENT. 



CHARLES BABBAGE, ESQ. 




LONDON: 



JOHN MURRAY, ALBEMARLE STREET. 



MDCCC XXXVII. 



/S37 



/° m<se Lib, 



CONTENTS. 



Page 



Preface 



V 



Chapter I. 



Nature of the Argument 



23 



Chapter II. 

Argument in favour of Design from the changing of 



Chapter III. 

Argument to show that the Doctrines in the preced- 
ing Chapter do not lead to Fatalism .... 50 

Chapter IV. 

On the Account of the Creation, in the First Chapter 

of Genesis 63 



Laws in Natural Events 



.30 



B 



ii 



CONTENTS. 



Chapter V. 

Page 

Further View of the same Subject 72 

Chapter VI. 

Of the Desire of Immortality 82 

Chapter VII. 

On Time 88 

Chapter VIII. 

Argument from Laws intermitting — on the Nature of 

Miracles 93 

Chapter IX. 

On the permanent Impression of our Words and 

Actions on the Globe we inhabit 109 

Chapter X. 

On Hume's Argument against Miracles . . . . 118 

Chapter XI. 

A priori Argument in favour of the Occurrence of 

Miracles 133 

Chapter XII. 

Thoughts on the Nature of Future Punishments . 143 



CONTENTS. i 
Chapter XIII. 

Page 

Reflections on Free Will 151 

Chapter XIV. 

Thoughts on the Origin of Evil 156 

Conclusion 157 



APPENDIX. 

Note A. On the great Law which regulates Matter . 163 

B. On the Calculating Engine 170 

C. Extract from the Theory of Probabilities 

of La Place 173 

D. Note to Chap. VIII. on Miracles ... 175 

E. Note to Chap. X. on Hume's Argument 

against Miracles 176 

F. On the Consequences of Central Heat . . 182 

G. On the Action of Existing Causes in pro- 

ducing Elevations and Subsidences in 
Portions of the Earth's Surface . . . 187 

H. Tables showing the Expansion of Beds of 

Granite variously heated 198 

I. Extracts from Letters of Sir John Herschel 202 
b 2 



LV 



CONTENTS. 



Page 

K. Or. the Elevation of Beaches by Tides . . 218 

L. On Ripple Mark 222 

M. On the Age of Strata, as inferred from the 

Rings of Trees embedded in them . . 226 

N. On a Method of multiplying Illustrations 

from Wood- Cuts 235 



PREFACE. 



The volume here presented to the public does 
not form a part of that series of works com- 
posed at the desire of the trustees who directed 
the application of the bequest of £8000, by 
the late Earl of Bridge water, for the purpose 
of advancing arguments in favour of Natural 
Religion. 



Vi PREFACE. 

I have, however, thought, that in furthering 
the intentions of the testator, by publishing 
some reflections on that subject, I might be 
permitted to connect with them a title which 
has now become familiarly associated, in the 
public mind, with the evidences in favour of 
Natural Religion. 

The Bridgewater Treatises were restricted by 
the founder to the subject of Natural Religion ; 
and I had intended not to have deviated from 
their example. In the single instance in which 
the question of miracles has been discussed, I 
'was led so irresistibly, by the very nature of the 
illustrations employed in the former argument, 
to the view there proposed, that I trust to 
being excused for having ventured one step 
beyond the strict limits of that argument, by 
entering on the first connecting link between 
natural religion and revelation. 

The same argument will produce very various 



PREFACE. Vii 

degrees of conviction on different minds ; 
and much of this difference will depend on 
the extent of previous information, and on 
the strength of the reasoning faculty in those 
to whom the argument is addressed. To the 
great variety, therefore, of the illustrations 
which have been adduced in proof of design 
and of benevolence in the works of the 
Creator, there can be no objection. In truth, 
to the cultivated eye of science 3 the origin and 
consequences of the mightiest hurricane, as 
well as those of the smallest leaf it scatters 
in its course, equally lead to the inference 
of a designing power, the more irresistibly 
the more extensive the knowledge which is 
brought to bear on those phenomena. 

One of the chief defects of the Treatises 
above referred to appears to me to arise from 
their not pursuing the argument to a suffi- 
cient extent. When a multitude of appa- 
rently unconnected facts is traced up to some 



Viii PREFACE. 

common principle, we feel spontaneously an 
admiration for him who has explained to us 
the connexion ; and if, advancing another 
stage in the investigation, he prove that other 
facts, apparently at variance with that prin- 
ciple, are not merely no exceptions, but are 
themselves inevitable consequences of its ap- 
plication, our admiration of the principle, 
and our respect for its discoverer, are still 
further enhanced. 

But if this respect and admiration are 
yielded to the mere interpreter of Nature's 
laws, how much more exalted must those 
sentiments become when applied to the Being 
who called such principles into living exist- 
ence by creating matter subservient to their 
dominion — whose mind, intimately cognizant 
of the remotest consequences of the present 
as well as of all other laws, decreed existence 
to that one alone, which should comprehend 
within its grasp the completion of its destiny — 



PREFACE. ix 

which should require no future intervention 
to meet events unanticipated by its author, in 
whose omniscient mind we can conceive no 
infirmity of purpose — no change of intention ! 

The object of these pages, as of the Bridge- 
water Treatises, is to show that the power and 
knowledge of the great Creator of matter and 
of mind are unlimited. Deeply engaged in 
those other pursuits from which my chief argu- 
ments are drawn, I regret the impossibility of 
bestowing on their full development that time 
and attention which the difficulty and import- 
ance of the subject equally deserve ; and in 
committing these fragments to the press, 
perhaps in too condensed a form, I wish them 
to be considered merely as suggestions in- 
tended to direct the reader's attention to lines 
of argument which appear to me new, and to 
views of nature which appear more magnifi- 
cent, than those with which I was previously 
acquainted. 



X PREFACE. 

Probably I should not have been induced 
to place my reflections on the subject before 
the public, had I not, in common with other 
cultivators of the more abstract branches of 
mathematical science, felt that a prejudice, 
which I had believed to have been long eradi- 
cated from every cultivated mind, had lately 
received support, at least to a certain extent, 
from a chapter in the first* of the Bridgewater 
Treatises ; and in a still greater degree, from 
a work of a far different order — one, however, 
which derived its only claim to notice from the 
circumstance of its appearing under the sanc- 
tion of the University of Oxford. 

The prejudice to which I allude is, that the 
pursuits of science are unfavourable to religion. 

There are two classes of men most deeply 
impressed with the conviction of the very 



* It was the first in the order of publication. 



PREFACE. Xi 

limited extent of human knowledge — those 
whose contracted information renders them 
eminent examples of the fact, and those whose 
wide grasp of many of its profoundest branches 
has taught them, by lengthened experience, that 
each accession to their stock but enables them 
to view a larger portion of its illimitable field. 
Those who belong to the first of these classes 
must acquire the alphabet of science, in order 
to understand knowledge, and the elements 
of modesty, to use it with dignity. When 
they have thus graduated in the i( infant 
school" of philosophy, they may perhaps 
understand the argument, and perchance be 
worthy of a reply, — but not till then. 

In that chapter of the first Bridgewater 
Treatise to which I have referred, the charge 
seems not even to be limited to those who 
pursue that branch of science which is con- 
versant with the properties of pure number, 
and with abstractions of a like nature, but 



xii 



PREFACE. 



applies to all who cultivate deductive processes 
of reasoning. 

It is maintained by the author, that long 
application to such inquiries disqualifies the 
mind from duly appreciating the force of that 
kind of evidence which alone can be adduced 
in favour of Natural Theology. 

" We may thus, with the greatest propriety, deny to the 
mechanical philosophers and mathematicians of recent times 
any authority with regard to their views of the administra- 
tion of the universe ; we have no reason whatever to expect 
from their speculations any help, when we ascend to the 
first cause and supreme ruler of the universe. But we 
might perhaps go farther, and assert that they are in some 
respects less likely than men employed in other pursuits, 
to make any clear advance towards such a subject of specu- 
lation." — Bridgewater Treatise, by ^cRev. Wm. Whewell, 
p. 334. 

Admitting, for the sake of argument, that 
there have been individuals, possessed of high 
intellectual powers, successfully devoted to 
those subjects, who have arrived by reasoning 
at conclusions respecting the First Cause, 



PREFACE. Xiii 

totally opposite to those entertained by Mr. 
Whewell and myself, I should still be very 
reluctant to endeavour to invalidate the in- 
fluence of their conclusions, by any inquiry 
either into their intellectual or their moral 
character. Reasoning is to be combated and 
refuted by reasoning alone. Any endeavour to 
raise a prejudice, or throw the shadow of an 
imputation, either implies the existence of 
some latent misgiving in the minds of those 
who employ such weapons, or is a tacit admis- 
sion that the question is beyond the grasp of 
one at least of the debaters. 

Who that has studied their works ever 
dreamed of inquiring into the moral or intel- 
lectual character of Euclid or Archimedes, for 
the purpose of confirming or invalidating his 
belief in their conclusions ? Who that pos- 
sesses confidence in his own reason, justified 
by a laborious cultivation and successful 
exercise of that faculty, fails to anatomize and 



XIV PREFACE. 

refute the arguments, rather than analyze the 
mental or moral habits of those from whom he 
differs ? 

The only case in which such extraneous 
matters can be fairly called in, is when facts 
are stated resting on testimony. Then it is 
not only just, but it is necessary for the 
sake of truth, to inquire into the habits of 
mind of him by whom they are adduced ; — 
whether he possesses sufficient talent and 
precision to enable him to state precisely 
what his senses convey to him, and nothing 
more; or, if he receive information from 
others, whether he is credulous or cautious. 
In both cases, it is necessary to inquire into 
moral feelings, in order to be assured that 
there is no wilful mis-statement in the 
groundwork of his reasoning. And even 
when this is well established, it is still ne- 
cessary to inquire whether he had any 
personal, professional, or pecuniary interest 



PREFACE. XV 

which may insensibly have influenced his 
mind in one direction. 

Such I conceive to be the sound distinction 
between those branches of knowledge resting 
on facts open to the observation of all, sup- 
ported by reasoning addressed to the under- 
standings of all, — and those other branches 
in which reasoning is mixed up with testi- 
mony. In the former, the argument is every 
thing — the character nothing: in the latter, 
the character must be sifted as well as the 
arguments. 

Feeling convinced that the truths of Natural 
Religion rest on foundations far stronger than 
those of any human testimony ; that they are 
impressed in indelible characters, by almighty 
power, on every fragment of the material 
world, I cannot but regret that reflections 
should have been made, in connexion with 
this subject, calculated to throw the least 



Xvi PREFACE. 

shadow of doubt on evidence otherwise irre- 
sistible. 

As, however, these views of the nature of 
the question may not bring that conviction 
to other minds, which they do to my own, 
and as one of the disturbing forces which act 
on our minds has been strongly put forward, 
it is but justice* to state the whole of them. 
It requires but little insight into man's 
heart to perceive that profession and pro- 
fessional advancement — that power and 
wealth — have a far more frequent and more 
effective influence on his judgment than any 
mental habits he may be supposed to have 
cultivated. 

It may be right then to state, that the 
author of these pages has always been an ardent 
but not an exclusive cultivator of some of 
the more abstract branches of mathematical 
science. In pursuing one of those inquiries, 



PREFACE. XVU 

amongst the most recondite and apparently 
the most removed from any practical applica- 
tion, he was struck with the bearing of some 
of the results which presented themselves, on 
the question of Natural Religion ; and these 
he has endeavoured to place before the reader, 
in the following pages. 

The author belongs to no profession in 
which he can hope for advancement, if he suc- 
cessfully advocate one side of the question, or 
in which his prospects can be injured by can- 
didly stating any arguments on the other. 
He has not been invited by men high in the 
State, and deservedly respected, to support 
that great basis which precedes all revelation, 
and on which it must all rest. Nor has any 
sum of money been assigned to him, that, 
whatever the mercantile success or failure 
of the present volume may be, he shall, 
on its publication, reap a large pecuniary 
reward. 

c 



XV111 



PREFACE. 



Having chosen a career to which the insti- 
tutions of the country hold out none of those 
great prizes that stimulate professional exer- 
tions, and which constrain men to yield a cer- 
tain degree of deference to the opinions, sound 
or unsound, of their countrymen, he has, on 
the one hand, nothing to hope from their ap- 
probation, and, on the other, is equally exempt 
from any fear of their censure ; and, had his 
conviction been as strongly opposed to the 
doctrines this Fragment advocates, as it is in 
their favour, he would, had a fit occasion 
presented itself, fearlessly have laid before the 
world the arguments which had forced his 
mind to that conviction. 

In conclusion, I have to express to my fel- 
low-labourers in the cause, my hope that they 
will put no unkind interpretation on these re- 
marks, which, founded on principles of human 
nature, are necessarily of general application ; 
that they will see that motives alien, in my 



PREFACE. Xix 

own opinion, to the subject, having been once 
introduced, candour to those who differ from 
us, as well as a deference to truth itself, com- 
pelled me to state them fully. 

CHARLES BABBAGE. 



Dorset-street, 
Manchester- square, 
April 1837. 



The following account of the origin of the Bridge- 
water Treatises, is extracted from one of these 
works : — 

" The Right Honourable and Reverend Francis Henry, Earl of 
Bridgewater, died in the month of February, 1829; and, by his 
last will and testament, bearing date the 25 th of February, 1825, 
he direcled certain Trustees therein named, to invest in the public 
funds the sum of eight thousand pounds sterling ; this sum, with 
the accruing dividends thereon, to be held at the disposal of 
the President, for the time being, of the Royal Society of London, 
to be paid to the person or persons nominated by him. The tes- 
tator further directed, that the person or persons selected by the 
said President should be appointed to write, print, and publish, 
one thousand copies of a work " On the Power, Wisdom, and 
Goodness of God, as manifested in the Creation ;" illustrating such 
work by all reasonable arguments, as, for instance, the variety 
and formation of God's creatures in the animal, vegetable, and 
mineral kingdoms; the effect of digestion, and thereby of conver- 
sion; the construction of the hand of man, and an infinite variety 
of other arguments : as also by discoveries, ancient and modern, 
in arts, sciences, and the whole extent of literature. He desired, 
moreover, that the profits arising from the sale of the works 
so published should be paid to the authors of the works. 

The late President of the Royal Society, Davies Gilbert, Esq., 
requested the assistance of his Grace the Archbishop of Canterbury, 
and of the Bishop of London, in determining upon the best mode 
of carrying into effect the intentions of the testator. Acting with 
their advice, and with the concurrence of a nobleman immediately 
connected with the deceased, Mr. Davies Gilbert appointed eight 
gentlemen to write separate Treatises on the different branches of 
the subject." 



xxii 



Of the eight gentlemen so appointed, four were of 
the clerical, and four of the medical, profession. 
Their names, and the subjects assigned to them, are 
as follows: — 

1. The Rev. Thomas Chalmers, D.D., Professor of Divinity in 

the University of Edinburgh — " On the Adaptation of Ex- 
ternal Nature to the Moral and Intellectual Constitution 
of Man." 

2. The Rev. Wm. Buckland, D.D., F.R.S., Canon of Christ 

Church, and Professor of Geology in the University of 
Oxford — "On Geology and Mineralogy." 

3. The Rev. Wm. Whewell, M.A., F.R.S., Fellow of Trinity 

College,Cambridge — " OnAstronomy andGeneral Physics." 

4. The Rev. Wm. Kirby, M.A., F.R.S.— " On the History, 

Habits, and Instincts of Animals." 



5. John Kidd, M.D., F.R.S., Regius Professor of Medicine in 

the University of Oxford — " On the Adaptation of Ex- 
ternal Nature to the Physical Condition of Man." 

6. Sir Charles Bell, K.H., F.R.S.— " The Hand : its Me- 

chanism and Vital Endowments, as evincing Design." 

7. Peter Mark Roget, M.D., Fellow of, and Secretary to, the 

Royal Society — "On Animal and Vegetable Physiology." 

8. Wm. Prout, M.D., F.R.S.— " On Chemistry, Meteorology, 

and the Function of Digestion." 



CHAP. I. 



NATURE OF THE ARGUMENT. 



The notions we acquire of contrivance and 
design arise from comparing our observations 
on the works of other beings with the inten- 
tions of which we are conscious in our own 
undertakings. We take the highest and best of 
human faculties, and, exalting them in our 
imagination to an unlimited extent, endeavour 
to attain an imperfect conception of that 
Infinite Power which created every thing 
around us. In pursuing this course, it is 
evident that we are liable to impress upon the 



24 INTRODUCTION. 

notion of Deity thus shadowed out, many- 
traces of those imperfections in our own 
limited faculties which are best known to 
those who have most deeply cultivated them. 
It is also evident that all those discoveries 
which arm human reason with new power, and 
all additions to our acquaintance with the 
material world, must from time to time render 
a revision of that notion necessary. The 
present seems to be a fit occasion for such a 
revision. 

Many excellent and religious persons not 
deeply versed in what they mistakenly call 
" human knowledge" but which is in truth the 
interpretation of those laws that God himself 
has impressed on his creation, have endea- 
voured to discover proofs of design in a 
multitude of apparent adaptations of means 
to ends, and have represented the Deity as 
perpetually interfering, to alter for a time the 
laws he had previously ordained; thus by 
implication denying to him the possession 



INTRODUCTION. 



25 



of that foresight which is the highest attribute 
of omnipotence. Minds of this order, insen- 
sible of the existence of that combining and 
generalising faculty which gives to human 
intellect its greatest development, and tied 
down by the trammels of their own peculiar 
pursuits, have in their mistaken zeal not per- 
ceived their own unfitness for the mighty task, 
and have ventured to represent the Creator 
of the universe as fettered by the same 
infirmities as those by which their own limited 
faculties are subjugated. To causes of this 
kind must in some measure be attributed an 
opinion which has been industriously spread, 
that minds highly imbued with mathematical 
knowledge are disqualified, by the possession 
of that knowledge, and by the habits of mind 
produced during its acquisition, from rightly 
appreciating the works of the Creator. 

At periods and in countries in which the 
knowledge of the priests exceeded that of the 
people, science has always been held up by the 



26 



INTRODUCTION. 



former class as an object of regard, and its 
crafty possessors have too frequently defiled its 
purity by employing their knowledge for the 
delusion of the people. On the other hand, 
at times and in countries in which the know- 
ledge of the people has advanced beyond 
that of the priesthood, the ministers of the 
temple have too often been afraid of the 
advance of knowledge, and have threatened 
with the displeasure of the Almighty those 
engaged in employing the faculties he has 
bestowed on the study of the works he has 
created. At the present period, when know- 
ledge is so universally spread that neither 
class is far in advance of the other, — when 
every subject is submitted to unbounded 
discussion, — when it is at length fully acknow- 
ledged that truth alone can stand unshaken by 
perennial attacks, and that error, though for 
centuries triumphant, must fall at last, and 
leave behind no ashes from which it may 
revive, the authority of names has but little 
weight : facts and arguments are the basis of 



INTRODUCTION. 



27 



creeds, and convictions so arrived at are the 
more deeply seated, and the more enduring, 
because they are not the wild fancies of pas- 
sion or of impulse, but the deliberate results 
of reason and reflection. 

It is a condition of our race that we must 
ever wade through error in our advance 
towards truth ; and it may even be said that 
in many cases we exhaust almost every variety 
of error before we attain the desired goal. 
But truths, once reached by such a course, 
are always most highly valued ; and when, in 
addition to this, they have been exposed to 
every variety of attack which splendid talents 
quickened into energy by the keen perception 
of personal interests can suggest, — when they 
have revived undying from unmerited neglect ; 
when the anathema of spiritual, and the arm 
of secular power have been found as impotent 
in suppressing, as their arguments were in 
refuting them, then they are indeed irre- 
sistible. Thus tried and thus triumphant in 



28 



INTRODUCTION. 



the fiercest warfare of intellectual strife, even 
the temporary interests and furious passions 
which urged on the contest, have contributed 
in no small measure to establish their value, 
and thus to render these truths the permanent 
heritage of our race. 

Viewed in this light, the propagation of an 
error, although it may be unfavourable or 
fatal to the temporary interest of an individual, 
can never be long injurious to the cause of 
truth. It may, at a particular time, retard its 
progress for a while, but it repays the trans- 
itory injury by a benefit as permanent as the 
duration of the truth to which it was opposed. 
This reasoning is offered for the purpose of 
proving that the toleration of the fullest dis- 
cussion is most advantageous to truth. It is 
not offered as the advocate of or the apology 
for error ; and whilst it is admitted that every 
person who wilfully puts forward as valid an 
argument the soundness of w T hich he doubts, 
incurs a deep responsibility, it is also some 



INTRODUCTION. 



29 



satisfaction to reflect that the delay thus occa- 
sioned to the great cause can be but small, 
and that those who in sincerity of heart main- 
tain arguments which a more advanced state 
of knowledge shall prove to be erroneous, may 
yet ultimately contribute, by that very publi- 
cation, to its speedier establishment. 



* 



CHAP. II. 



ARGUMENT IN FAVOUR OF DESIGN FROM THE 
CHANGING OF LAWS IN NATURAL EVENTS. 

The estimate we form of the intellectual 
capacity of our race, is founded on an exa- 
mination of those productions which have 
resulted from the loftiest flights of individual 
genius, or from the accumulated labours of 
generations of men, by whose long-continued 
exertions a body of science has been raised 
up, surpassing in its extent the creative powers 
of any individual, and demanding for its deve- 
lopment a length of time, to which no single 
life extends. 



ARGUMENT IN FAVOUR OF DESIGN. 31 

The estimate we form of the Creator of the 
visible world rests ultimately on the same 
foundation. Conscious that we each of us em- 
ploy, in our own productions, means intended 
to accomplish the objects at which we aim, and 
tracing throughout the actions and inventions 
of our fellow- creatures the same intention, — 
judging also, of their capacity by the fit selec- 
tion they make of the means by which they 
work, we are irresistibly led, when we con- 
template the natural world, to attempt to 
trace each existing fact presented to our senses 
to some precontrived arrangement, itself per- 
haps the consequence of a yet more general 
law; and where the most powerful aids by 
which we can assist our limited faculties fail in 
enabling us to detect such connexions, we still, 
and not the less, believe that a more extended 
inquiry, or higher powers, would enable us to 
discover them. 

The larger the number of consequences 
resulting from any law, and the more they are 
foreseen, the greater the knowledge and intel- 



32 



ARGUMENT IN 



ligence we ascribe to the being by which it 
was ordained. In the earlier stages of our 
knowledge, we behold a multitude of distinct 
laws, all harmonizing to produce results which 
we deem beneficial to our own species : as 
science advances/ many of these minor laws 
merge into some more general principles ; and 
with its higher progress these secondary prin- 
ciples appear, in their turn, the mere conse- 
quences of some still more general law. Such 
has been the case in two of the most curious 
and most elaborately cultivated branches of 
human knowledge, the sciences of astronomy 
and optics* All analogy leads us to infer, and 
new discoveries continually direct our expecta- 
tion to the idea, that the most extensive laws 
to which we have hitherto attained, converge to 
some few simple and general principles, by 
which the whole of the material universe is 
sustained, and from which its infinitely varied 
phenomena emerge as the necessary conse- 
quences.* 

* See Note A in the Appendix. 



FAVOUR OF DESIGN. 



33 



To illustrate the distinction between a sys- 
tem to which the restoring hand of its con- 
triver is applied, either frequently or at distant 
intervals, and one which had received at its 
first formation the impress of the will of its 
author, foreseeing the varied but yet neces- 
sary laws of its action, throughout the whole 
extent of its existence, we must have recourse 
to some machine, the produce of human skill. 
But far as all such engines must ever be 
placed at an immeasurable interval below 
the simplest of Nature's works, yet, from the 
vastness of those cycles which even human 
contrivance in some cases unfolds to our view, 
we may perhaps be enabled to form a faint 
estimate of the magnitude of that lowest step 
in the chain of reasoning, which leads us up 
to Nature's God. 

The illustration which I shall here employ 
will be derived from the results afforded by 
the Calculating Engine ;* and this I am the 

* The reader will find a short account of this engine in 
the Appendix, Note B. 

D 



34 



ARGUMENT IN 



more disposed to use, because my own views 
respecting the extent of the laws of Nature 
were greatly enlarged by considering it, and 
also because it incidentally presents matter 
for reflection on the subject of inductive 
reasoning. Nor will any difficulty arise from 
the complexity of that engine ; no knowledge 
of its mechanism, nor any acquaintance with 
mathematical science, being necessary for 
comprehending the illustration, it being suffi- 
cient merely to conceive that computations of 
great complexity can be effected by me- 
chanical means. 

Let the reader imagine that such an engine 
has been adjusted; and that it is moved by a 
weight ; and that he sits down before it, and 
observes a wheel, which revolves through a 
small angle round its axis, at short intervals, 
presenting to his eye, successively, a series 
of numbers engraved on its divided circum- 
ference. 



FAVOUR OF DESIGN. 



35 



Let the figures thus seen be the series 1, 2, 
3, 4, 5, &c, of natural numbers, each of which 
exceeds its immediate antecedent by unity. 

Now, reader, let me ask how long you will 
have counted before you are firmly convinced 
that the engine has been so adjusted that it 
will continue whilst its motion is maintained, 
to produce the same series of natural numbers ? 
Some minds are so constituted, that after 
passing the first hundred terms, they will be 
satisfied that they are acquainted with the 
law. After seeing five hundred terms, few will 
doubt ; and after the fifty-thousandth term 
the propensity to believe that the succeeding 
term will be fifty thousand and one, will be 
almost irresistible. That term will be fifty 
thousand and one ; and the same regular suc- 
cession will continue ; the five-millionth and 
the fifty-millionth term will still appear in 
their expected order ; and one unbroken chain 
of natural numbers will pass before your eyes, 
from one up to one hundred million. 

d 2 



36 



ARGUMENT IN 



True to the vast induction which has been 
made, the next succeeding term will be one 
hundred million and one ; but the next num- 
ber presented by the rim of the wheel, in- 
stead of being one hundred million and two, 
is one hundred million ten thousand and two. 
The whole series from the commencement 
being thus : — 

1 

2 
3 
4 
5 



99,999,999 
100,000,000 
regularly as far as 100,000,001 

100,010,002 the law changes 

100,030,003 

100,060,004 

100,100,005 

100,150,006 

100,210,007 

100,280,008 



FAVOUR OF DESIGN. 



37 



The law which seemed at first to govern this 
series fails at the hundred million and second 
terra. This term is larger than we expected, 
by 10,000. The next term is larger than was 
anticipated, by 30,000, and the excess of each 
term above what we had expected forms the 
following table : — 

10,000 

30,000 

60,000 
100,000 
150,000 

being, in fact, the series of triangular num- 
bers* each multiplied by 10,000. 

* The numbers 1, 3, 6, 10, 15, 21, 28, &c. are formed 
by adding the successive terms of the series of natural 
numbers thus ; 

1 = I. 

1+2 = 3. 
1+2 + 3 = 6. 
1 + 2 + 3 + 4 = 10, &c. 
They are called triangular numbers, because a number 
of points corresponding to any term can always be placed 
in the form of a triangle, for instance : — 



1 3 



6 10 



38 



ARGUMENT IN 



If we now continue to observe the num- 
bers presented by the wheel, we shall find, 
that for a hundred, or even for a thousand 
terms, they continue to follow the new law 
relating to the triangular numbers ; but after 
watching them for 2761 terms, we find that 
this law fails in the case of the 2762d term. 

If we continue to observe, we shall discover 
another law then coming into action, which 
also is dependent, but in a different manner, 
on triangular numbers. This will continue 
through about 1430 terms, when a new law is 
again introduced, which extends over about 
950 terms ; and this too, like all its prede- 
cessors, fails, and gives place to other laws, 
which appear at different intervals. 

Now it must be remarked, that the law 
that each number presented by the Engine is 
greater by unity than the preceding number, 
which law the observer had deduced from an 
induction of a hundred million instances, was 



FAVOUR OF DESIGN. 



39 



not the true law that regulated its action ; and 
that the occurrence of the number 100,010,002 
at the 100,000, 002d term, was as necessary a 
consequence of the original adjustment, and 
might have been as fully foreknown at the 
commencement, as was the regular succession 
of any one of the intermediate numbers to 
its immediate antecedent. The same remark 
applies to the next apparent deviation from 
the new law, which was founded on an in- 
duction of 2761 terms, and also to the suc- 
ceeding law ; with this limitation only — that 
whilst their consecutive introduction at various 
definite intervals is a necessary consequence 
of the mechanical structure of the engine, our 
knowledge of analysis does not enable us to 
predict the periods themselves at which the 
more distant laws will be introduced. 

Such are the facts which, by a certain ad- 
justment of the Calculating Engine, would be 
presented to the observer. Now, let him ima- 
gine another engine, offering to him precisely 



40 



ARGUMENT IN 



the same figures in the same order of suc- 
cession ; but let it be necessary for the maker 
of that other engine, previously to each appa- 
rent change in the law, to make some new 
adjustment in the structure of the engine itself, 
in order to accomplish the ends proposed. 
The first engine must be susceptible of having 
embodied in its mechanical structure, that 
more general law of which all the observed 
laws were but isolated portions, — a law so 
complicated, that analysis itself, in its present 
state, can scarcely grasp the whole question. 
The second engine might be of far simpler 
contrivance ; it must be capable of receiving 
the laws impressed upon it from without, but 
is incapable, by its own intrinsic structure, of 
changing, at definite periods, and in unlimited 
succession, those laws by which it acts. 
Which of these two engines would, in the 
reader's opinion, give the higher proof of skill 
in the contriver? He cannot for a moment 
hesitate in pronouncing that that on which, 
after its original adjustment, no superintend- 



FAVOUR OF DESIGN. 



41 



ance was required, displayed far greater in- 
genuity than that which demanded, at every 
change in its law, the intervention of its 
contriver. 

The engine we have been considering is but 
a very small portion (about fifteen figures) 
of a much larger one, which was preparing, 
and partly executed ; it was intended, when 
completed, that it should have presented at 
once to the eye about one hundred and thirty 
figures. In that more extended form which 
recent simplifications have enabled me to give 
to machinery constructed for the purpose of 
making calculations, it will be possible, by cer- 
tain adjustments, to set the engine so that it 
shall produce the series of natural numbers in 
regular order, from unity up to a number ex- 
pressed by more than a thousand places of 
figures. At the end of that term, another and a 
different law shall regulate the succeeding 
terms ; this law shall continue in operation per- 
haps for a number of terms, expressed by unity, 



42 



ARGUMENT IN 



followed by a thousand zeros, or 10 1000 ; at 
which period another law shall be introduced, 
and, like its predecessors, govern the figures 
produced by the engine during a third of those 
enormous periods. This change of laws might 
continue without limit ; each individual law 
destined to govern for millions of ages the cal- 
culations of the engine, and then give way to 
its successor to pursue a like career.* 

Thus a series of laws, each simple in itself, 
successively spring into existence, at distances 
almost too great for human conception. The 
full expression of that wider law, which com- 
prehends within it this unlimited sequence of 
minor consequences, may indeed be beyond 
the utmost reach of mathematical analysis : 
but of one remarkable fact, however, we are 

* It has been supposed that ten turns of the handle of the 
calculating engine might be made in a minute, or about five 
hundred and twenty-six millions in a century. As in 
this case, each turn would make a calculation, after the lapse 
of a million of centuries, only the fifteenth place of figures 
would have been reached. 



FAVOUR OF DESIGN. 



43 



certain — that the mechanism brought into 
action for the purpose of changing the nature 
of the calculation from the production of its 
more elementary operations into those highly 
complicated ones of which we speak, is itself 
of the simplest kind. 

In contemplating the operations of laws so 
uniform during such immense periods, and 
then changing so completely their apparent 
nature, whilst the alterations are in fact only 
the necessary consequences of some far higher 
law, we can scarcely avoid remarking the 
analogy which they bear to several of the 
phenomena of nature. 

The laws of animal life which regulate the 
caterpillar, seem totally distinct from those 
which, in the subsequent stage of its existence, 
govern the butterfly. The difference is still 
more remarkable in the transformations un- 
dergone by that class of animals which spend 
the first portion of their life beneath the sur- 
face of the waters, and the latter part as 



44 



ARGUMENT IN 



inhabitants of air. It is true that the periods 
during which these laws exist are not, to our 
senses, enormous, like the mechanical ones 
above mentioned; but it cannot be doubted 
that, immeasurably more complex as they are, 
they were equally foreknown by their Author : 
and that the first creation of the egg of the 
moth, or the libellula, involved within its 
contrivance, as a necessary consequence, the 
whole of the subsequent transformations of 
every individual of their respective races. 

In turning our views from these simple con- 
sequences of the juxtaposition of a few wheels, 
it is impossible not to perceive the parallel 
reasoning, as applied to the mighty and far 
more complex phenomena of nature. To call 
into existence all the variety of vegetable 
forms, as they become fitted to exist, by the 
successive adaptations of their parent earth, is 
undoubtedly a high exertion of creative power. 
When a rich vegetation has covered the globe, 
to create animals adapted to that clothing, 



FAVOUR OF DESIGN. 



45 



which, deriving nourishment from its luxuri- 
ance, shall gladden the face of nature, is not 
only a high but a benevolent exertion of 
creative power. To change, from time to time, 
after lengthened periods, the races which exist, 
as altered physical circumstances may render 
their abode more or less congenial to their 
habits, by allowing the natural extinction of 
some races, and by a new creation of others 
more fitted to supply the place previously 
abandoned, is still but the exercise of the same 
benevolent power. To cause an alteration in 
those physical circumstances — to add to the 
comforts of the newly created animals — all 
these acts imply power of the same order, a 
perpetual and benevolent superintendence, to 
take advantage of altered circumstances, for the 
purpose of producing additional happiness. 

But, to have foreseen, at the creation of 
matter and of mind, that a period would ar- 
rive when matter, assuming its prearranged 
combinations, would become susceptible of 



46 



ARGUMENT IN 



the support of vegetable forms; that these 
should in due time themselves supply 
the pabulum of animal existence ; that suc- 
cessive races of giant forms or of micro- 
scopic beings should at appointed periods 
necessarily rise into existence, and as inevi- 
tably yield to decay; and that decay and 
death — the lot of each individual existence 
— should also act with equal power on the 
races which they constitute ; that the extinc- 
tion of every race should be as certain as the 
death of each individual ; and the advent of 
new genera be as inevitable as the destruc- 
tion of their predecessors ; — to have foreseen 
all these changes, and to have provided, by 
one comprehensive law, for all that should 
ever occur, either to the races themselves, to 
the individuals of which they are composed, 
or to the globe which they inhabit, manifests 
a degree of power and of knowledge of a far 
higher order. 



The vast cycles in the geological changes 



FAVOUR OF DESIGN. 



47 



that have taken place in the earth's surface, 
of which we have ample evidence, offer 
another analogy in nature to those mechanical 
changes of law from which we have endea- 
voured to extract a unit sufficiently large to 
serve as an imperfect measure for some of 
the simplest works of the Creator. 

The gradual advance of Geology, during the 
last twenty years, to the dignity of a science, 
has arisen from the laborious and extensive 
collection of facts, and from the enlightened 
spirit in which the inductions founded on those 
facts have been deduced and discussed. To 
those who are unacquainted with this science, 
or indeed to any person not deeply versed in 
the history of this and kindred subjects, it is 
impossible to convey a just impression of the 
nature of that evidence by which a multitude 
of its conclusions are supported : — evidence 
in many cases so irresistible, that the records 
of the past ages, to which it refers, are traced 
in language more imperishable than that of 



48 



ARGUMENT IN 



the historian of any human transactions ; the 
relics of those beings, entombed in the strata 
which myriads of centuries have heaped upon 
their graves, giving a present evidence of their 
past existence, with which no human testi- 
mony can compete. It is found that each 
additional step, in the grouping together of 
the facts of geology, confirms the view that 
the changes of our planet, since it has been 
the abode of man, is but as a page in the 
massive volumes of its history, every leaf of 
which, written in the same character, conveys 
to the decypherer the idea of a succession 
of the same causes acting with varying inten- 
sity, through unequal but enormous periods, 
each period apparently distinguished by the 
coming in or going out of new subsidiary laws, 
yet all submitted to some still higher con- 
dition, which has stamped the mark of unity 
on the series, and points to the conclusion 
that the minutest changes, as well as those 
transitions apparently the most abrupt, have 
throughout all time been the necessary, the 



FAVOUR OF DESIGN. 49 

inevitable consequences of some more com- 
prehensive law impressed on matter at the 
dawn of its existence. 



E 



50 



ARGUMENT 



CHAP. III. 

ARGUMENT TO SHOW THAT THE DOCTRINES IN 
THE PRECEDING CHAPTER DO NOT LEAD TO 
FATALISM. 

If all the combinations and modifications 
of matter can be supposed to be traced up to 
one general and comprehensive law, from 
which every visible form, both in the organic 
and inorganic world flows, as the necessary 
consequence of the first impression of that 
law upon matter, it might seem to follow that 
Fate or Necessity governs all things, and that 
the world around us may not be the result of 
a contriving mind working for a benevolent 
purpose. 



AGAINST FATE. 



51 



Such, possibly, may be the first impression 
of this view of the subject ; but it is an er- 
roneous view, — one of those, perhaps, through 
which it is necessary to pass, in order to arrive 
at truth. Let us briefly review the labour 
which the human race has expended, in at- 
taining the limited knowledge we possess. For 
about six thousand years man has claimed 
the earth as his heritage, and asserted his 
dominion over all other beings endued with 
life ; yet, during a large portion of that period, 
how comparatively small has been his mental 
improvement ! Until the invention of print- 
ing, the mass of mankind were in many re- 
spects almost the creatures of instinct. It is 
true, the knowledge possessed by each gene- 
ration, instead of being the gift of Nature, 
was derived from the instruction of their prede- 
cessors; but, how little were those lessons 
improved by repeated communication ! Trans- 
mitted most frequently by unenlightened in- 
structors, they might lose, but could rarely 
gain in value. 

e 2 



52 



ARGUMENT 



Before the invention of printing, acci- 
dental position determined the opinions and 
the knowledge of the great mass of mankind. 
Oral information being almost the only kind 
accessible, each man shared the opinions of 
his kindred and neighbours ; and truth, which 
is ever most quickly and most surely elicited 
by discussion, lost all those advantages which 
diversity of opinion always produces for it. The 
minds of individual men, however powerful, 
could address themselves only to a very small 
portion of their fellow men ; their influence 
was restricted by space and limited by time, 
and their highest powers were not stimulated 
into action by the knowledge that their reason- 
ings could have effect where their voices were 
unheard, or by the conviction that the truths 
they arrived at, and the discoveries they 
made, would extend beyond their country, 
and survive their age. 

But, since the invention of printing, how 
different has been the position of mankind ! 



AGAINST FATE. 



53 



the nature of the instruction no longer de- 
pends entirely on the knowledge of the 
instructor. The village school-master com- 
municates to his pupils the power of using 
an instrument by which not merely the best 
of their living countrymen, but the greatest 
and wisest men of all countries and all times, 
may become their instructors. Even the ele- 
mentary writings through which this art is 
taught, give to the pupil, not the sentiments of 
the teacher, but those which the public opinion 
of his countrymen esteems most fit for the be- 
ginner in knowledge. Thus the united opinions 
of multitudes of human minds are brought 
to bear even upon seemingly unimportant 
points. 

If such is the effect of the invention of 
printing upon ordinary minds, its influence 
over those more highly endowed is far greater. 
To them the discussion of the conflicting opi- 
nions of different countries and distant ages, 
and the establishment of new truths, presents 



54 



ARGUMENT 



a field of boundless and exalted ambition. 
Advancing beyond the knowledge of their 
neighbours and countrymen, they may be ex- 
posed to those prejudices which result from 
opinions long stationary ; but encouraged by 
the approbation of the greatest of other na- 
tions, and the more enlightened of their own, — 
knowing that time alone is wanting to complete 
the triumph of truth, they may accelerate the 
approaching dawn of that day which shall 
pour a flood of light over the darkened intel- 
lects of their thankless countrymen — content 
themselves to exchange the hatred they expe- 
rience from the honest and the dishonest into- 
lerance of their contemporaries, for that higher 
homage, alike independent of space and of time, 
which their memory will for ever receive 
from the good and the gifted of all countries 
and all ages. 

Until printing was very generally spread, 
civilisation scarcely advanced by slow and lan- 
guid steps ; since this art has become cheap, 



AGAINST FATE. 



55 



its advances have been unparalleled, and its 
rate of progress vastly accelerated. 

It has been stated by some, that the civili- 
sation of the Western World has resulted from 
its being the seat of the Christian religion : 
however much the mild tenor of its doctrines 
is calculated to assist in producing such an 
effect, that religion cannot but be injured by an 
unfounded statement. It is to the easy and 
cheap methods of communicating thought from 
man to man, which enable a country to sift, as 
it were, its whole people, and to produce, in its 
science, its literature, and its arts, not the 
brightest efforts of a limited class, but the 
highest exertions of the most powerful minds 
among a whole community ; — it is this which 
has given birth to the wide-spreading civilisa- 
tion of the present day, and which promises a 
futurity yet more prolific. Whoever is ac- 
quainted with the present state of science and 
the mechanical arts, and looks back over the 
inventions and civilisation which the fourteen 



56 



ARGUMENT 



centuries subsequent to the introduction of 
Christianity have produced, and compares 
them with the advances made during the suc- 
ceeding four centuries following the invention 
of printing, will have no doubt as to the effec- 
tive cause. 

It is during these last three or four centu- 
ries, that man, considered as a species, has 
commenced the development of his intellec- 
tual faculties — that he has emerged from a po- 
sition in which he was almost the creature of 
instinct, to a state in which every step in ad- 
vance facilitates the progress of his succes- 
sors. In the first period, arts were discovered 
by individuals, and lost to the race ; in the 
latter, the diffusion of ideas enabled the rea- 
soning of one class to unite with the observa- 
tions of another, and the most advanced point 
of one generation became the starting post 
of the next. 

It is during this portion of our history that 



AGAINST FATE. 



57 



man has become acquainted with his real posi- 
tion in the universe — that he has measured the 
distance from that which is to us the great 
fountain of light and heat — that he has traced 
the orbits of earth's sister spheres, and calcu- 
lated the paths of all their dependent worlds — 
that he has arrived at the knowledge of a 
law — that of gravity, which appears to go- 
vern all matter, and whose remotest conse- 
quences, if first traced by his telescope, are 
found written in his theory ; or, if first pre- 
dicted by his theory, are verified by his obser- 
vations. 

Simple as that law now appears, and beau- 
tifully in accordance with all the observations of 
past and of present times, consider what it has 
cost of intellectual study. Copernicus, Galileo, 
Kepler, Euler, Lagrange, Laplace, all the great 
names which have exalted the character of 
man, by carrying out trains of reasoning 
unparalleled in every other science ; these, 
and a host of others, each of whom might 



58 ARGUMENT 

have been the Newton of another field, have 
all laboured to work out, the consequences 
which resulted from that single law which 
he discovered. All that the human mind has 
produced— the brightest in genius, or the most 
continuous in application, has been lavished 
on the details of the law of gravity. 

Had that law been other than it is — had it 
been the inverse cube of the distance, for 
example, it would still have required an equal 
expense of genius and of perseverance to have 
worked out its details. But, between the laws 
represented by the inverse square, and the 
inverse cube of the distance, there are inter- 
posed an infinite number of other laws, each 
of which might have been the basis of a 
system requiring the most extensive know- 
ledge to trace out its consequences. Between 
every law which can be expressed by whole 
numbers, whether it be direct or inverse, 
an infinity of others can still be interposed. 
All these might be again combined by two, 



AGAINST FATE. 



59 



by three, or by any other combinations, and 
new systems might be imagined,* submitted 
to such laws. Thus, another infinity of laws, 
of a far higher order — in fact, of an infinitely 
higher order — might again be added to the list. 
And this might still be increased by every other 
combination, of which such laws admit, besides 
that by addition, to which we have already 
alluded, thus forming an infinity itself of so 
high an order, that it is difficult to conceive. 
Man has, as yet, no proof of the impossibility 
of the existence of any of these laws. Each 
might, for any reason we can assign, be the 
basis of a creation different from our own. 

It is at this point that skill and knowledge 
re-enter the argument, and banish for ever the 
dominion of chance. The Being who called 

* Even beyond this, every law so imagined might be 
interrupted by any discontinuous function ; and thus be 
made to agree, for any period, with laws of simpler form, 
and yet deviate, in one single, or in a certain limited num-f 
ber of cases, and then agree with it for ever. 



60 



ARGUMENT 



into existence this creation, of which we are 
parts, must have chosen the present form, the 
present, laws, in preference to the infinitely 
infinite variety which he might have willed 
into existence. He must have known and fore- 
seen all, even the remotest consequences of 
every one of those laws, to have penetrated 
but a little way into one of which has ex- 
hausted the intellect of our whole species. 

But, if such is the view we must take of the 
knowledge of the Creator, when contemplating 
the laws of inanimate matter — laws into whose 
consequences it has cost us such accumulated 
labour to penetrate — what language can we 
speak, when we consider that the laws which 
connect matter with animal life may be as in- 
finitely varied as those which regulate material 
existence ? The little we know, might, per- 
haps, lead us to infer a far more unlimited 
field of choice. The chemist has reduced all 
the materials of the earth with which we 
are acquainted, to about fifty simple bodies ; 



AGAINST FATE. 



61 



but the zoologist can make no such reductions 
in his science. He must claim for one scarcely 
noticed class — that of intestinal parasites — 
about thirty thousand species ; and, not to 
mention the larger classes of animals, who shall 
number the species of infusoria in living waters, 
still less those which are extinct, and whose 
scarcely visible relics are contained within the 
earth, in almost mountain masses.* 

In absolute ignorance of any — even the 
smallest link of those chains which bind life 
to matter, or that still more miraculous one, 
which connects mind to both, we can only 
pursue our path by the feeble light of analogy, 
and humbly hope that the Being, whose power 

* Professor Ehrenberg, of Berlin, has discovered that the 
tripoli employed in that city for polishing metals, which is 
dug up at Bilin, in Bohemia, consists almost entirely of the 
siliceous remains of infusoria, of a species so minute, that 
about 41,000 millions of them weigh 220 grains, and oc- 
cupy the space of a cubic inch. The reader will find a 
translation of the highly interesting papers of Professor 
Ehrenberg, in the third number of the " Scientific Me- 
moirs," published by Mr. R. Taylor. 



62 



ARGUMENT AGAINST FATE. 



and benevolence are unbounded, may enable 
us, in some further stage of our existence, to 
read another page in the history of his mighty 
works. 

Enough, however, and more than enough, 
may be gathered even from our imperfect 
acquaintance with matter, and some few of its 
laws, to prove the unbounded knowledge 
which must have preceded their organization. 



ACCOUNT OF THE CREATION. 



63 



CHAP. IV. 

ON THE ACCOUNT OF THE CREATION, IN THE FIRST 
CHAPTER OF GENESIS. 

A strange and singular argument has fre- 
quently been brought against the truth of the 
facts presented to us by Geology, — facts which 
every instructed person may confirm by the 
evidence of his senses. It has been stated 
that they cannot be true ; because, if admitted, 
they lead inevitably to the conclusion, that the 
earth has existed for an enormous period, 
extending, perhaps, over millions of years ; 
whereas, it was supposed, from the history of 
the creation as delivered by Moses, that the 



64 



MOSAIC ACCOUNT 



earth was first created about six thousand 
years ago. 

A different interpretation has been lately 
put upon that passage of the sacred writings ; 
and, according to the highest authorities of 
the present time, it was not the intention of 
the writer of the book of Genesis to assign this 
date to the creation of our globe, but only to 
that of its most favoured inhabitants. 

Now, it is obvious that additional observations, 
and another advance in science, may at no 
distant period render necessary another inter- 
pretation of the Mosaic narrative ; and this 
again, at a more remote time, may be superseded 
by one more in accordance with the existing 
knowledge of that day. And thus, the authority 
of Scripture will be gradually undermined by 
the weak though well-intentioned efforts of its 
friends in its support. For it is clear that 
when a work, translated by persons most 
highly instructed in its language, and seeking, 



OF THE CREATION. 



65 



in plainness and sincerity, to understand its 
true meaning, admits of such discordant inter- 
pretations, it can have little authority as a 
history of the past, or a guide to the future. 

It is time, therefore, to examine this ques- 
tion by another light, and to point out to 
those who support what is called the literal 
interpretation of Scripture, the precipice to 
which their doctrines, if true, would inevitably 
lead ; and to show, not by the glimmerings of 
elaborate criticism, but by the plainest prin- 
ciples of common sense, that there exists no 
such fatal collision between the words of Scrip- 
ture and the facts of nature. 

And first, let us examine what must of 
necessity be the conclusion of any candid 
mind from the mass of evidence presented to 
it. Looking solely at the facts in which all 
capable of investigation agree — facts which it 
is needless to recite, they having been so fully 
and ably stated in the works of Mr. Lyell and 

F 



66 



MOSAIC ACCOUNT 



Dr. Buckland, — we there see, and with no 
theoretic eye, the remains of animated beings, 
more and more differing from existing races, as 
we descend in the series of strata. Not merely 
are the petrified bones preserved, displaying 
marks of the insertion of every muscle neces- 
sary for the movement of the living animal, 
but in some cases we discover even the secre- 
tions of their organs, prepared either for nou- 
rishment or for defence. Almost every stratum 
we pause to examine, affords indubitable evi- 
dence of having, at some former period, existed 
for ages at the bottom of some lake or estuary, 
some inland sea, or some extensive ocean 
teeming with animal existence, or of having 
been the surface of a country covered with 
vegetation, which perished and was renewed 
at distant and successive periods. 

Those, however, who, without the know- 
ledge which enables them to form an opinion 
on the subject, feel any latent wish that this 
evidence should be overthrown, would do 



OF THE CREATION. 



G7 



well to remember that geology also furnishes 
strong evidence in favour of the much more 
direct statement of Moses, as to the recent 
creation of man. And although we must ever 
feel a certain degree of caution in admitting 
negative evidence as conclusive ; yet, in the 
present instance, the multitude of fossil bones 
which have been discovered, and which, when 
examined by persons duly qualified for the 
task, have been uniformly pronounced to be 
those of various tribes of animals, and not 
those of the human race, undoubtedly affords 
strong corroborative evidence in confirmation 
of the Mosaic account. 

In truth, the mass of evidence which combines 
to prove the great antiquity of the earth, is so 
irresistible, and so unshaken by any opposing 
facts, that none but those who are alike inca- 
pable of observing the facts and of appreciating 
the reasoning, can for a moment conceive the 
present state of its surface to have been the 
result of only six thousand years of existence. 

F 2 



68 



MOSAIC ACCOUNT 



What, then, have those accomplished who 
have restricted the Mosaic account of creation 
to that diminutive period, which is, as it were, 
but a span in the duration of the earth's ex- 
istence, and who have imprudently rejected 
the testimony of the senses, when opposed to 
their philological criticisms ? Undoubtedly, if 
they have succeeded in convincing either them- 
selves or others, that one side of the question 
must be given up as untenable ; those who 
are so convinced are bound to reject that 
w 7 hich rests on testimony, not that which is 
supported by still existing facts. The very 
argument which Protestants have opposed to 
the doctrine of transubstantiation,* would, if 

* The historian of the " Decline of the Roman Empire," 
carried the argument yet further ; — 

" I still remember (he remarks) my solitary transport at 
" the discovery of a philosophical argument against tran- 
" substantiation ; that the text of Scripture which seems to 
" indicate the real presence is attested only by a single 
" sense — our sight ; while the real presence itself is disproved 
»< by three of our senses — the sight, the touch, the taste." — 
Gibbon s Memoirs of his Life, vol. i. p. 58. 



OF THE CREATION. 



69 



their view of the case were correct, be equally 
irresistible against the book of Genesis. 

But let us consider what would be the con- 
clusion of every reasonable being in a parallel 
case. Let us imagine a manuscript written 
three thousand years ago, and professing to 
be a revelation from the Deity, in which it 
was stated that the colour of the paper of the 
very book now in the reader's hands is black, 
and that the colour of the ink in the charac- 
ters which he is now reading is white : — with 
that reasonable doubt of his own individual 
faculties which would become the inquirer into 
the truth of a statement said to be derived from 
so high an origin, he would ask of all those 
around him, whether to their senses the paper 
appeared to be black and the ink to be white: 
If he found the senses of other individuals 
agree with his own, then he would undoubt- 
edly pronounce the alleged revelation a for- 
gery, and those who propounded it to be either 
deceived or deceivers. He would rightly ini- 



70 



MOSAIC ACCOUNT 



pute the attempted deceit to moral turpitude, 
to the gross ignorance or to the interested mo- 
tives of the supporters of it ; and he certainly 
would not commit the impiety of supposing the 
Deity to have wrought a miraculous change 
upon the senses of our whole species, and to 
demand their belief in a fact directly opposed 
to those senses — thus throwing doubt upon 
every conclusion of reason which related to 
external objects, and amongst others, upon the 
very evidence by which the authenticity of that 
questionable manuscript was itself supported, 
and even of its very existence when before 
their eyes. 

Thus, then, had those who attempt to show 
that the account of the creation, in the book of 
Genesis, is contradicted by the discoveries of 
modern science, succeeded, they would have 
destroyed the testimony of Moses— they would 
have uncanonised one portion of Scripture, and 
by implication have thrown doubt on the re- 
mainder. But minds which thus failed to trace 



OF THE CREATION. 



71 



out the necessary consequences of their own 
argument, were not likely to have laid very 
secure foundations for the basis on which it 
rested ; and I shall presently prove that the 
contradiction they have imagined can have no 
real existence ; and that whilst the testimony 
of Moses remains unimpeached, we may also 
be permitted to confide in the testimony of 
our senses. 



72 



MOSAIC ACCOUNT 



CHAP. V. 



FURTHER VIEW OF THE SAME SUBJECT. 



Before entering on the main argument it 
may be remarked, that the plainest and most 
natural view of the language employed by the 
sacred historian of the earth is, that his ex- 
pressions ought to be received by us in the 
sense in which they were understood by the 
people to whom he addressed himself. If, when 
speaking of the creation, instead of using the 
terms light and water, he had spoken of the 
former as a wave, and of the latter as the union 
of two invisible airs, he would assuredly have 



OF THE CREATION. 



73 



been perfectly unintelligible to his country- 
men. At the distance of above three thousand 
years his writings would just have begun to be 
comprehended, and possibly three thousand 
years hence those views may be as inappli- 
cable to the then existing state of human 
knowledge as they would have been when the 
first chapter of Genesis was written. 

Those, however, who attempt to disprove 
the facts presented by observation, by placing 
them in opposition to revelation, have mistaken 
the very groundwork of the question. The 
revelation of Moses itself rests, and must ne- 
cessarily rest, on testimony. Moses, the author 
of the oldest of the sacred books, lived about 
fifteen hundred years before the christian era, 
or about three thousand three hundred years 
ago. The oldest manuscripts of the Pentateuch 
at present known, appear to have been written 
about 900 years ago.* These were copied from 

* Mr. Home, in the Introduction to the Critical Study of 



74 



MOSAIC ACCOUNT 



others of older date, and those again might 
probably, if their history were known, be traced 
up through a few transcripts to the original 

the Holy Scriptures, states, that the total number of He- 
brew MSS. collated by Dr. Kennicott, for his critical edi- 
tion of the Hebrew Bible, was about 630. In that work, 
Mr. Horne gives an account of ten of the most ancient of 
these MSS. : three of which contain the first chapter of 
Genesis, viz. : — 

No. 4. Codex Csesense, in the Malatesta Library at 
Bologna, written about the end of the eleventh century. 

No. 6. Codex Mediolanensis, written towards the close 
of the twelfth century. " The beginning of the book of 
" Genesis, and the end of Leviticus and Deuteronomy, 
u have been written by a later hand." 

No. 8. Codex Parisiensis, 27, about the commencement 
of the twelfth century. 

No. 10. Codex Parisiensis, 24, written at the beginning 
of the twelfth century. 

In the same work is an account of six of the most ancient 
of the four hundred and seventy-nine collated by M. De 
Rossi. Two of these contain the first chapter of Ge- 
nesis ; and the date of both is about the end of the eleventh 
or beginning of the twelfth century. 

Of the Manuscripts of the Samaritan versions of the Pen- 
tateuch, cited in the same work — one the Codex 197, in 
the Ambrosian Library at Milan — Dr. Kennicott thinks that 
it is certainly not later than the tenth century. 



OF THE CREATION. 



75 



author ; but no part of this is revelation ; it is 
testimony. Although the matter which the 
book contains was revealed to Moses, the fact 
that what we now receive as revelation is 
the same with that originally communicated 
revelation, is entirely dependent on testimony. 
Admitting, however, the full weight of that 
evidence, corroborated as it is by the Samaritan 
version ; nay, even supposing that we now 
possessed the identical autograph of the book 
of Genesis by the hand of its author, a most 
important question remains, — What means do 
we possess of translating it ? 

In similar cases we avail ourselves of the 
works of the immediate predecessors, and of 
the contemporaries of the writer ; but here we 
are acquainted with no work of any prede- 
cessor, — of no writing of any contemporary ; 
and we do not possess the works of any 
writers in the same language, even during se- 
veral succeeding centuries, if we except some 
few of the sacred books. How, then, is it 



76 



MOSAIC ACCOUNT 



possible to satisfy our minds of the minute 
shades of meaning of words, perhaps employed 
popularly ; or, if they were employed in a 
stricter and more philosophical sense, where 
are the contemporary philosophical writings 
from which their accurate interpretation may 
be gained ? 

The extreme difficulty of such an inquiry 
will be made apparent by imagining a parallel 
case. Let us suppose all writings in the 
English, and indeed in all other languages pre- 
vious to the time of Shakespeare, to have been 
destroyed ; — let us imagine one manuscript of 
his plays to remain, but not a vestige of the 
works of any of his contemporaries; and further, 
suppose the whole of the succeeding works of 
English literature to be annihilated nearly up 
to the present time. Under such circumstances, 
what would be our knowledge of Shakespeare ? 
We should undoubtedly understand the ge- 
neral tenor and the plots of his plays. We 
should read the language of all his characters ; 



OF THE CREATION. 77 

and viewing it generally, we might even be 
said to understand it. But how many words 
connected with the customs, habits, and man- 
ners of the time must, under such circum- 
stances, necessarily remain unknown to us ! 
Still further, if any question arose, requiring 
for its solution a knowledge of the minute 
shades of meaning of words now long obsolete, 
or of terms supposed to be used in a strict or 
philosophical sense, how completely unsatis- 
factory must our conclusions remain ! Such 
I conceive to be the view which common sense 
bids us take of the interpretation of the book 
of Genesis. The language of the Hebrews, 
in times long subsequent to the date of that 
book, may not have so far changed as to pre- 
vent us from rightly understanding generally 
the history it narrates ; but there appears to 
be no reasonable ground for venturing to pro- 
nounce with confidence on the minute shades 
of meaning of allied words, and on such foun- 
dations to support an argument opposed to the 
evidence of our senses. 



78 



MOSAIC ACCOUNT 



I should have hesitated in offering these 
remarks respecting the right interpretation of 
the Mosaic account of the creation, had the ar- 
gument depended on any acquaintance with the 
language in which the sacred volume is writ- 
ten, or on any refinements of criticism, had 
I possessed that knowledge ; but in estimating 
its validity, or in supplying a more cogent 
argument, I intreat the reader to consider 
well the difficulties which it is necessary to 
meet. 

1st. The Church of England, if we may 
judge by the writings of those placed in autho- 
rity, has hitherto considered it to have been 
expressly stated in the book of Genesis, that 
the earth was created about six thousand 
years ago. 

2dly. Those observers and philosophers 
who have spent their lives in the study of 
Geology, have arrived at the conclusion that 
there exists irresistible evidence, that the date 



OF THE CREATION. 



79 



of the earth's first formation is far anterior to 
the epoch supposed to be assigned to it by 
Moses ; and it is now admitted by all compe- 
tent persons, that the formation even of those 
strata which are nearest the surface must have 
occupied vast periods — probably millions of 
years — in arriving at their present state. 

3dly. Many of the most distinguished mem- 
bers of the Church of England now distinctly 
and formally admit the fact of such a length- 
ened existence of the earth we inhabit ; for it 
is so stated in the eighth Bridgemater Treatise, 
a work written by the Professor of Geology in 
the University of Oxford — himself holding an 
office of dignity in that Church, and expressly 
appointed to write upon that subject, by the 
Archbishop of Canterbury, and the Bishop of 
London. 

4thly. The Professor of Hebrew at the same 
University has proposed a new interpretation 
of those passages of the Book of Genesis, 



80 



MOSAIC ACCOUNT 



which were hitherto supposed to be adverse to 
the now admitted facts. 

Such being the present state of the case ; — 
it surely becomes a duty to require a very high 
degree of evidence, before we again claim au- 
thority for the opinion that the book of Genesis 
contains such a precise account of the work of 
the creation, that we may venture to appeal to 
it as a refutation of observed facts. The history 
of the past errors of our parent Church sup- 
plies us with a lesson of caution which ought 
not to be lost by its reformed successors. 
The fact that the venerable Galileo was com- 
pelled publicly to deny, on bended knee, a 
truth of which he had the most convincing de- 
monstration, remains as a beacon to all after 
time, and ought not to be without its influence 
on the inquiring minds of the present day. 

If the explanation offered by the Pro- 
fessor of Hebrew be admitted, those who 
adhere to it must still have some misgivings 



OF THE CREATION. 



81 



as to the effect of new discoveries in nature 
causing continual occasion for amended trans- 
lations of various texts ; whereas, should the 
view which has been advocated in this chap- 
ter be found correct, instead of fearing that the 
future progress of science may raise additional 
difficulties in the way of revealed religion, 
we are at once relieved from all doubt on that 
subject. 







82 



THE DESIRE 



CHAP. VI. 

OF THE DESIRE OF IMMORTALITY. 

That wish, universally expressed in every 
variety of form, of remaining in the memory 
of our fellow-creatures after our passage from 
the present scene, has rightly been adduced as 
evidence of the desire of immortality, and has 
sometimes been explained as being founded on 
an instinctive belief that we are destined to 
it by the Creator. 

The hope of remaining embalmed in the 
fond recollection of those we held most dear 
in life, and even of being remembered by our 



OF IMMORTALITY. 



83 



more immediate descendants, has something 
in it nearly connected with self; but the wish 
for more extended reputation, — the desire that 
our name should pass in after times from 
mouth to mouth, cherished and admired by 
those whose applause is won by no personal 
recollections : or the still more fervent aspira- 
tions, that we may stamp indelibly on the age 
we live in some mark of our individual exist- 
ence which shall form an epoch in the history 
of man : these hopes, these longings, receive 
no interpretation from the all-dominant prin- 
ciple of self; unless indeed we suppose the 
sentient principle of our nature not merely 
existing, but also conscious of, and gratified 
by, the earthly immortality it had achieved. 
Yet the more distant and the higher the objects 
we pursue, the less is it possible to suppose the 
mind, so occupied on earth, can, in another 
stage of its existence, derive pleasure from such 
perceptions. 



To support this opinion, it is only necessary 
g 2 



84 



THE DESIRE 



to examine the states of mind in the various 
classes of the aspirants after fame. 



Through every form of society, and through 
every rank of each, may be traced this uni- 
versal passion. Examine the most highly civi- 
lized inhabitants of earth ; search through it 
for the most cultivated and refined in taste ; 
for the most sagacious in penetrating the pas- 
sions of mankind, the most skilful in wielding 
them, or the most powerful in intellectual 
might. Taste, feeling, passion, ambition, ge- 
nius, severed or combined, equally yield obedi' 



OF IMMORTALITY. 85 

ence to its sway, and present, under different 
appearances, the effects of its all-controlling 
power. 



Look at the highest productions of the poet 
or the novelist. By connecting his story with 
the scenery, the traditions, or the history of 
his country, he may ensure for it a local inte- 
rest, a domestic and transitory popularity ; but 
it is that deeper penetration into the secrets 
of the human heart, which enables him to 
select from amongst the same materials, those 
feelings that are common to the race which 



86 THE DESIRE 

have, as occasion called them forth, appeared, 
and will continue to reappear, as long as the 
same affections and passions shall continue to 
animate and agitate our frames. 



From the examination of these its highest 
forms, we may gather some common principles, 
and be enabled to perceive that the love of 
fame is far different from that passion for vul- 
gar applause with which it is too frequently 



OF IMMORTALITY. 



87 



confounded. We may learn, that the higher 
the intellectual powers devoted to the task, 
the more remote the period for which ambition 
delights to raise its far distant altar. 



88 ON TIME. 



CHAP. V1L 



ON TIME. 



Time and change are great, only with re- 
ference to the faculties of the beings which 
note them. The insect of an hour, which 
flutters, during its transient existence, in an 
atmosphere of perfume, would attribute un- 
changing duration to the beautiful flowers 
of the cistus, whose petals cover the dewy 



ON TIME. 89 

grass but a few hours after it has received 
the lifeless body of the gnat. These flowers, 
could they reflect, might contrast their trans- 
itory lives with the prolonged existence of 
their greener neighbours. The leaves them- 
selves, counting their brief span by the lapse 
of a few moons, might regard as almost 
indefinitely extended the duration of the com- 
mon parent of both leaf and flower. The 
lives of individual trees are lost in the con- 
tinued destruction and renovation which take 
place in forest masses. Forests themselves, 
starved by the exhaustion of the soil, or con- 
sumed by fire, succeed each other in slow 
gradation. A forest of oaks waves its lux- 
uriant branches over a spot which has been 
fertilized by the ashes of a forest of pines. 
These periods again merge into other and still 
longer cycles, during which the latest of a 
thousand forests sinks beneath the waves, from 
the gradual subsidence of its parent earth ; or in 
which extensive inundations, by accumulating 
the silt of centuries, gradually convert the 



90 



ON TIME. 



living trunks into their stony resemblances. 
Stratum upon stratum subsides in comminuted 
particles, and is accumulated in the depths of 
the ocean, whence they again arise, consoli- 
dated by pressure or by fire, to form the con- 
tinents and mountains of a new creation. 

Such, in endless succession, is the history of 
the changes of the globe we dwell upon ; and 
human observation, aided by human reason, 
has as yet discovered few signs of a be- 
ginning — no symptom of an end. Yet, in 
that more extended view which recognises 
our planet as one amongst the attendants of 
a central luminary ; that sun itself the soul, 
as it were, of vegetable and animal existence, 
but an insignificant individual among its 
congeners of the milky way : — when we re- 
member that that cloud of light, gleaming 
with its myriad systems, is but an isolated 
nebula amongst a countless host of rivals, 
which the starry firmament surrounding us 
on all sides, presents to us in every varied 



ON TIME, 



91 



form ; — some as uncondensed masses of atte- 
nuated light; — some as having, in obedience 
to attractive forces, assumed a spherical figure ; 
others, as if farther advanced in the history of 
their fate, having a denser central nucleus 
surrounded by a more diluted light, spreading 
into such vast spaces, that the whole of our 
own nebula would be lost in it : — others there 
are, in which the apparently unformed and 
irregular mass of nebulous light is just curd- 
ling, as it were, into separate systems ; whilst 
many present a congeries of distinct points of 
light, each, perhaps, the separate luminary of 
a creation more glorious than our own ; — when 
the birth, the progress, and the history of 
sidereal systems are considered, we require 
some other unit of time than even that com- 
prehensive one which astronomy has unfolded 
to our view. Minute and almost infinitesimal 
as is the time which comprises the history of 
our race compared with that which records 
the history of our system, the space even of 



92 



ON TIME. 



this latter period forms too limited a stan- 
dard wherewith to measure the footmarks of 
eternity. 



93 



CHAP. VIII. 



ARGUMENT FROM LAWS INTERMITTING ON THE 
NATURE OF MIRACLES. 



The object of the present chapter is to 
show that miracles are not deviations from 
the laws assigned by the Almighty for the 
government of matter and of mind ; but that 
they are the exact fulfilment of much more 
extensive laws than those we suppose to 
exist. In fact, if we were endued with 
acuter senses and higher reasoning faculties, 
they are the very points we should seek to 
observe, as the test of any hypothesis we had 
been led to frame concerning the nature of 



94 LAWS INTERMITTING. 

those laws. Even with our present imperfect 
faculties we frequently arrive at the highest 
confirmation of our views of the laws of na- 
ture, by tracing their actions under singular 
circumstances. 

The mode by which I propose to arrive at 
these conclusions is, by appealing to the judg- 
ment which each individual will himself form, 
when examining that piece of mere human 
mechanism, to which the argument so fre- 
quently compels me to advert. If he shall 
agree with me, that the second of the two 
views presented to him exhibits a higher de- 
gree of knowledge, and a higher exertion of 
power, than the first, he must inevitably con- 
clude, that the view here taken of the nature 
of a miracle, assigns a far higher degree of 
power and knowledge to the Deity. 

Let the reader again imagine himself sit- 
ting before the calculating engine, and let him 
again observe and ascertain, by lengthened 



NATURE OF MIRACLES. 



95 



induction, the nature of the law it is com- 
puting. Let him imagine that he has seen 
the changes wrought on its face by the lapse of 
thousands of years, and that, without one soli- 
tary exception, he has found the engine regis- 
ter the series of square numbers. Suppose, 
now, the maker of that machine to say to the 
observer, " I will, by moving a certain mecha- 
" nism, which is invisible to you, cause the 
" engine to make a cube number instead of a 
" square one, and then to revert to its former 
" course of square numbers;" the observer would 
be inclined to attribute to him a degree of 
power but little superior to that which was 
necessary to form the original engine. 

But, let the same observer, after the same 
lapse of time — the same amount of uninter- 
rupted experience of the uniformity of the law 
of square numbers, hear the maker of that en- 
gine say to him — " The next number which 
" shall appear on those wheels, and which 
" you expect to find a square number, shall 



96 



LAWS INTERMITTING. 



" not be such. When the machine was ori- 
" ginally ordered to make these calculations, 
" I impressed on it a law, which should coin- 
" cide with that of square numbers in every 
" case, except the one which is now about to 
" appear, after which no future exception can 
" ever occur ; but the unvarying law of the 
" squares shall be pursued until the machine 
ee itself perishes from decay." 

Undoubtedly the observer would ascribe a 
greater degree of power to the artist who thus 
willed that event at the distance of ages before 
its arrival. 

If the contriver of the engine then explain 
to him, that, by the very structure of it, he has 
power to order any number of such apparent 
deviations from its laws to occur at any future 
periods, however remote, and that each of 
these may be of a different kind ; and, if he 
also inform him, that he gave it that structure 
in order to meet events, which he foresaw must 



NATURE OF MIRACLES. 97 

happen at those respective periods, there can 
be no doubt that the observer would ascribe to 
the inventor far higher knowledge than if, 
when those events severally occurred, he were 
to intervene, and temporarily alter the calcu- 
lations of the machine. 

If, besides this, he were so far to explain the 
structure of the engine that the observer could 
himself, by some simple process, such as the 
mere moving of a bolt, call into action those 
apparent deviations whenever certain com- 
binations were presented to his eye ; if he 
were thus to impart a power of predicting 
such excepted cases, dependent on the will, 
although otherwise beyond the limits of the 
observer's power and knowledge, such a struc- 
ture would be admitted as evidence of a still 
more skilful contrivance. 

The engine which, in a former chapter, I 
introduced to the reader, possesses these 
powers. It may be set, so as to obey by any 

ii 



98 



LAWS INTERMITTING. 



given law ; and, at any periods, however re- 
mote, to make one or more seeming exceptions 
to that law. It is, however, to be observed, 
that the apparent law which the spectator ar- 
rived at, by an almost unlimited induction, is 
not the full expression of the law by which the 
machine acts ; and that the excepted case is 
as absolutely and irresistibly the necessary 
consequence of its primitive adjustment, as is 
any individual calculation amongst the count- 
less multitude. 

When the construction of that engine was 
first attempted, I did not seek to give to it 
the power of making calculations so far be- 
yond the reach of mathematical analysis as 
these appear to be : nor can I now foresee 
a probable period at which they may become 
practically available to human wants. I had 
determined to invest the invention with a de- 
gree of generality which should include a wide 
range of mathematical power ; and I was well 
aware that the mechanical generalisations 



NATURE OF MIRACLES. 



99 



I had organised contained within them much 
more than I had leisure to study, and some 
things which will probably remain unpro- 
ductive to a far distant day. 

Amongst those combinations which I was 
induced to examine, I observed the powers I 
have now recorded ; and the reflections they 
produced in my own mind, impelled me to pur- 
sue them for a time. If the reader agree with 
me in opinion, that these speculations have led 
to a more exalted view of the great Author of 
the universe than any we yet possessed, he 
must also have arrived at the conclusion, that 
the study of the most abstract branch of prac- 
tical mechanics, combined with that of the 
most abstruse portions of mathematical science, 
has no tendency to incapacitate the human 
mind from the perception of the evidences of 
natural religion ; and that even those very 
sources themselves furnish arguments which 
have opened more splendid views of the gran- 
deur of creation than any which the sciences 
ii 2 



100 



LAWS INTERMITTING. 



of observation or of physics have yet sup- 
plied. 

It may not, perhaps, be without its use to 
suggest another illustration respecting the na- 
ture of miracles. It is known that mathema- 
tical laws are sometimes expressed by curves. 
The figure 1 represents a re-entering curve of 
four dimensions, whose law of formation is 
given in the note.* A slight change in the na- 
ture of the constants makes it assume the form 
of fig. 2, which is still a continuous curve ; but 
a further change of the constants causes it to 
have two ovals, quite disconnected from the 
larger portion ; and, as the constants again 
alter, these ovals are reduced to points. 

* The equation 

— 4 f = - ax 4 + bx* + cx 2 + dx + e 
expresses several figures of an oval form, according to the 
nature of the roots of the equation, 

— ax 4 + bx 3 »f- cx 2 + dx + e = o. 
If its two lesser roots become imaginary, the curves, figures 
1, 2, 3, are produced. 



NATURE OF MIRACLES. 




NATURE OF MIRACLES. 



101 



In all four cases, every point in each branch 
of the curve obeys the same general law. The 
points, P and Q, invisible to the eye, are yet 
detected by mathematical analysis, and fulfil 
as precisely the original equation as any of the 
infinite number of other points, which consti- 
tute the rest of the curve. These points might 
be situated on the curve itself, and they are 
well known to mathematicians. It is to these 
singular points, which really fulfil the law of 
the curve, but which present to those who 
only judge of them by the organ of sight 
an apparent discontinuity, that I wish to 
call the attention, as offering an illustration 
of the doctrine here explained respecting 
miracles. 

It has been remarked, in the beginning of 
the present chapter, that it is to the singular 
points — to those points of such infinitely rare 
occurrence in a curve — that we frequently have 
recourse, as the test of our theories, for ex- 
plaining the phenomena of nature. 



104 



LAWS INTERMITTING. 



The existence, under peculiar circumstances, 
of conical refraction, was predicted by Sir W. 
Hamilton ; and, from an analytical investiga- 
tion into the nature of the curve surface, which 
represents the form of the luminiferous wave 
within the crystal, he ascertained that it had 
four conoidal cusps, at each of which there were, 
consequently, an infinite number of tangent 
planes. The course of the refracted ray being 
determined by the tangent plane to the wave 
surface, it followed that a single ray within the 
crystal, transmitted in the direction of the line 
joining two opposite cusps, corresponded to an 
infinite number of refracted rays without, con- 
stituting a refracted cone. 

The second case of conical refraction, pre- 
dicted by Sir William Hamilton, depended on 
another mathematical fact — namely, that the 
wave surface is touched in an infinite number 
of points, constituting a small circle of contact, 
by a single plane parallel to one of the circu- 
lar sections of the surface of elasticity. 



NATURE OF MIRACLES. 



105 



Professor Lloyd undertook to make the very 
delicate experiments required for this most 
interesting subject. Of the great importance 
of this investigation, Professor Lloyd was fully 
aware, for he remarks — 

" Here, then, are two singular and unex- 
" pected consequences of the undulatory theory, 
" not only unsupported by any facts hitherto 
" observed, but even opposed to all the analo- 
" gies derived from experience. If confirmed 
" by experiment, they would furnish new and 
* almost convincing proofs of that theory ; 
" and, if disproved, on the other hand, it is 
" evident that the theory must be abandoned 
" or modified.* 

On examining the first of these cases, expe- 
rimentally, the fact of conical refraction was 
fully established. But a new result now pre- 
sented itself: the rays of light thus conically 



* Trans, of Royal Irish Academy, Vol. XVII. 



106 



LAWS INTERMITTING. 



refracted were found to be polarized; and it 
was observed, that "the angle between the 
" planes of polarization of any two rays of 
" the cone was half the angle between the 
" planes, containing the rays themselves, and 
" the axis." 

This new law, thus approximately obtained 
by experiment, led the observer back to the 
theory ; and, on a further examination, he de- 
tected in that theory the very law he had just 
discovered by observation. 

The second case of conical refraction re- 
quired experiments of a still more delicate 
nature. They were, however, made, and suc- 
ceeded equally. The conically refracted ray 
was found to be polarised, according to the law 
which, in this instance, analysis had predicted; 
and, to complete the triumph of this union of 
theory and experiment, the measures in both 
cases, when made under proper circumstances, 
accorded with the theoretical conclusions, 



NATURE OF MIRACLES. 



107 



within such limits as might be fairly attributed 
to the necessary errors of observation. 

It is worthy of remark, that, at first, two 
facts presented themselves, which seemed at 
variance with the theory. In the first place, the 
emergent rays formed a solid cone, instead of 
a conical surface ; and, in the second place, the 
calculated angle, subtended by the sides of the 
cone, was only one half the observed angle. 
Both the facts were shown to depend upon 
the size of the aperture, and to arise from the 
rays which were inclined at small angles to the 
single theoretical direction. When the aper- 
ture was diminished, so as to be very small, (the 
case calculated by Sir William Hamilton,) then 
the cone of light became a conical surface, and 
the observed angle was the same as the calcu- 
lated one.* 

* Those who are acquainted with the history of astronomy, 
cannot fail to recall a parallel discrepancy between observa- 
tion and calculation in the theory of gravity. It appeared 
to result from that law, that the motion of the moon's 



108 



NATURE OF MIRACLES. 



apogee was only one half of what observation proved it to be ; 
and it is singular that Euler, D'Alembert, and Clairaut 
arrived, by different methods, at the same erroneous result ; 
and the truth of the great law of gravity appeared for a time 
to be doubtful. Clairaut, however, having assumed that 
the law of gravity contained a term only sensible at small 
distances (such as that of the moon), re-calculated the ques- 
tion, and finding it necessary, in consequence of this term, to 
push his approximation further than he had done, arrived 
at the conclusion, that the co-efficient of the new term va- 
nished ; and also, that the simple law of the inverse square 
of the distance, when the approximations were sufficiently 
pursued, gave the whole motions which observations had 
discovered. 



PERMANENT IMPRESSION OF WORDS. 109 



CHAP. IX. 

ON THE PERMANENT IMPRESSION OF OUR WORDS 
AND ACTIONS ON THE GLOBE WE INHABIT. 

The principle of the equality of action and 
reaction, when traced through all its conse- 
quences, opens views which will appear to many 
persons most unexpected. 

The pulsations of the air, once set in motion 
by the human voice, cease not to exist with 
the sounds to which they gave rise. Strong 
and audible as they may be in the immediate 
neighbourhood of the speaker, and at the 
immediate moment of utterance, their quickly 



110 THE PERMANENT IMPRESSION 

attenuated force soon becomes inaudible to 
human ears. The motions they have impressed 
on the particles of one portion of our atmo- 
sphere, are communicated to constantly in- 
creasing numbers, but the quantity of motion 
measured in the same direction receives no 
addition. Each atom loses as much as it 
gives, and regains again from others, portions 
of those motions which they in turn give up. 

The waves of air thus raised, perambulate 
the earth and ocean's surface, and in less than 
twenty hours every atom of its atmosphere 
takes up the altered movement due to that 
infinitesimal portion of the primitive motion 
which has been conveyed to it through count- 
less channels, and which must continue to in- 
fluence its path throughout its future exist- 
ence.* 

* La courbe decrite par une simple molecule d'air ou 
vapeurs est reglee d'une maniere aussi certain que les 
orbites planetaires : il n'y a de difference entre elles, que 



OF OUR WORDS. 



Ill 



But these aerial pulses, unseen by the 
keenest eye, unheard by the acutest ear, un- 
perceived by human senses, are yet demon- 
strated to exist by human reason ; and, in some 
few and limited instances, by calling to our 
aid the most refined and comprehensive in- 
strument of human thought, their courses are 
traced and their intensities are measured. If 
man enjoyed a larger command over mathe- 
matical analysis, his knowledge of these mo- 
tions would be more extensive ; but a being 
possessed of the unbounded knowledge of that 
science, would trace every the minutest conse- 
quences of that primary impulse. Such a 
being, however far exalted above our race, 
would yet be immeasurably below even our 
conception of infinite intelligence ; yet by him, 
supposing the original conditions of each atom 
of the atmosphere, as well as all the extraneous 
causes acting upon it to be given, its future and 
inevitable path would be clearly traced ; and 

celle qu'y met notre ignorance. — La Place, Thcorie Ana- 
lytique des Probabilitcs. Int. p. iv. 



112 THE PERMANENT IMPRESSION 

supposing the interference also of no new 
causes, the circumstances of the future history 
of the whole of the earth's atmosphere would 
be distinctly seen, and might be absolutely 
predicted for any even the remotest point of 
time. * 

Let us imagine a being, invested with such 
knowledge, to arrive at the predicted moment. 
If any the slightest deviation exists, he will 
immediately read in its existence the action 
of a new cause ; and, through the aid of the 
same analysis, tracing this discordance back 
to its source, he would become aware of the 
time of its commencement, and the point of 
space at which it originated. 

Thus considered, what a strange chaos is 
this wide atmosphere we breathe! Every 
atom impressed with good and with ill, re- 
tains at once the motions which philosophers 



* See Note C in the Appendix. 



OF OUR WORDS. 



113 



and sages have imparted to it, mixed and 
combined in ten thousand ways with all that is 
worthless and base. The air itself is one vast 
library, on whose pages are for ever written all 
that man has ever said or even whispered. 
There, in their mutable but unerring charac- 
ters, mixed with the earliest, as well as the 
latest sighs of mortality, stand for ever re- 
corded, vows unredeemed, promises unfulfilled, 
perpetuating in the united movements of each 
particle, the testimony of man's changeful 
will. 

But if the air we breathe is the never-failing 
historian of the sentiments we have uttered, 
earth, air, and ocean, are in like manner the 
eternal witnesses of the acts we have done. The 
same principle of the equality of action and 
reaction applies to them : whatever motion is 
communicated to any of their particles, is trans- 
mitted to all around it, the share of each being 
diminished by their number, and depending 
jointly on the number and position of those 

i 



114 THE PERMANENT IMPRESSION 

acted upon by the original source of disturbance. 
The waves of air, although in many instances 
sensible to the organs of hearing, are only ren- 
dered visible to the eye by peculiar contriv- 
ances ; whilst those of water offer to the sense 
of sight the most beautiful illustration of the 
transmission of motion. Every one who has 
thrown a pebble into the still waters of a shel- 
tered pool, has seen the circles it has raised 
gradually expanding in size, and as uniformly 
diminishing in distinctness. He may have ob- 
served the reflection of those waves from the 
edges of the pool. He may also have noticed 
the perfect distinctness with which two, three, 
or more series of waves each pursues its own 
unimpeded course, when diverging from two, 
three, or more centres of disturbance. He may 
have observed, that in such cases the particles 
of water where the waves intersect each other, 
partake of the movements due to each series. 

No motion impressed by natural causes, or 
by human agency, is ever obliterated. The 



OF OUR WORDS. 



115 



ripple on the ocean's surface caused by a gentle 
breeze, or the still water which marks the more 
immediate track of a ponderous vessel gliding 
with scarcely expanded sails over its bosom, 
are equally indelible. The momentary waves 
raised by the passing gale, apparently born but 
to die on the spot which saw their birth, leave 
behind them an endless progeny, which, reviv- 
ing with diminished energy in other seas, and 
visiting a thousand shores, reflected from each 
and perhaps again partially concentrated, pursue 
their ceaseless course till ocean be itself anni- 
hilated. 

The track of every canoe, of every vessel 
which has yet disturbed the surface of the 
ocean, whether impelled by manual force or 
elemental power, remains for ever registered 
in the future movement of all succeeding par- 
ticles which may occupy its place. The furrow 
which it left is, indeed, instantly filled up by 
the closing waters ; but they draw after them 
other and larger portions of the surrounding 

i2 



116 THE PERMANENT IMPRESSION 

element, and these again once moved, com- 
municate motion to others in endless succes- 
sion. 

The solid substance of the globe itself, whe- 
ther we regard the minutest movement of the 
soft clay which receives its impression from the 
foot of animals, or the concussion produced 
from falling mountains rent by earthquakes, 
equally retains and communicates, through all 
its countless atoms, their apportioned shares of 
the motions so impressed. 

Whilst the atmosphere we breathe is the ever- 
living witness of the sentiments we have uttered, 
the waters, and the more solid materials of the 
globe, bear equally enduring testimony of the 
acts we have committed. 

If the Almighty stamped on the brow of the 
earliest murderer, — the indelible and visible 
mark of his guilt, — he has also established laws 
by which every succeeding criminal is not less 



OF OUR WORDS. 



117 



irrevocably chained to the testimony of his 
crime ; for every atom of his mortal frame, 
through whatever changes its severed particles 
may migrate, will still retain, adhering to it 
through every combination, some movement 
derived from that very muscular effort, by 
which the crime itself was perpetrated. 



118 



hume's argument 



CHAP. X. 

on hume's argument against miracles. 

Few arguments have excited greater atten- 
tion, and produced more attempts at refutation, 
than the celebrated one of David Hume, re- 
specting miracles ; and it might be added, 
that more sophistry has been advanced against 
it, than its author employed in the whole of his 
writings. 

It must be admitted that in the argument, as 
originally developed by its author, there exists 
some confusion between personal experience 
and that which is derived from testimony ; and 
that there are several other points open to 
criticism and objection ; but the main argu- 



AGAINST MIRACLES. 



119 



ment, divested of its less important adjuncts, 
never has,, and never will be refuted. Dr. 
Johnson seems to have been of this opinion, 
as the following extract from his life by 
Boswell proves : — 

" Talking of Dr. Johnson's unwillingness to believe ex- 
traordinary things, I ventured to say — 

" ' Sir, you come near to Hume's argument against mira- 

* cles — That it is more probable witnesses should lie, or be 
1 mistaken, than that they should happen.' 

" Johnson. — ' Why, Sir, Hume, taking the proposition 
' simply, is right. But the Christian revelation is not proved 
' by miracles alone, but as connected with prophecies, and 
' with the doctrines in confirmation of which miracles were 

* wrought.' "* 

Hume contends that a miracle is a violation 
of the laws of nature ; and as a firm and 
unalterable experience has established these 
laws, the proof against a miracle from the very 
nature of the fact, is as entire as any argument 
from experience can possibly be imagined. 

* Boswell's Life of Johnson. Oxford, 1826. vol. iii. p. 169. 



120 



hume's argument 



" The plain consequence is (and it is a general maxim 
" worthy of our attention), that no testimony is sufficient 
" to establish a miracle, unless the testimony be of such a 
" kind, that its falsehood would be more miraculous than the 
" fact which it endeavours to establish : and even in that case 
" there is a mutual destruction of arguments, and the superior 
" only gives us an assurance suitable to that degree of force 
" which remains after deducting the inferior." * 

The difficulty which is frequently experi- 
enced in understanding this argument, appears 
to arise from the circumstance, that a double 
negative is concealed under the words " its 
falsehood would be more miraculous than" For 
in Hume's argument the word " miraculous" 
means improbable, although the improbability 
is of a very high degree. The clause then 
reads — 

Its falsehood would be more improbable than ; 

which is evidently equivalent to 

Its truth would be less improbable than ; 

which is again equivalent to 

Its truth would be more probable than. 



* Hume's Essays, Edinburgh, 1817, vol. ii. p. 117. 



AGAINST MIRACLES. 



121 



Replacing this in Hume's argument, it stands 
thus — 

" That no testimony is sufficient to establish a miracle, 
" unless the testimony be of such a kind, that its truth 
u would be more probable than the fact which it endea- 
" vours to establish." 

The argument is now reduced to the mere 
truism, that — 

The probability in favour of the testimony 
by which a miracle is supported, must be 
greater than the probability of the miracle itself. 

Before entering on the arguments I have to 
offer upon this point, it will be right to recall 
to the reader the view taken in a preceding 
chapter concerning the nature of miracles, and 
to compare it with that entertained by the 
acute philosopher whose essay I am venturing 
to criticise, lest, from any unperceived differ- 
ence in the employment of the term, I should 
inadvertently mislead both myself and my 
readers. 



122 



hume's argument 



It has been shown in the chapter above re- 
ferred to, that — A miracle may be only the 
exact fulfilment of a general law of nature, under 
such singular circumstances that to those imper- 
fectly acquainted with that law, it appears to be 
in direct opposition to it. The definition of a 
miracle adopted by Hume is this — 

" A miracle is a violation of the laws of nature." * 

And again, in note K — 

" A miracle may be accurately defined — A transgression 
" of a law of nature by a particular volition of the Deity, or 
" by the interposition oj some invisible agent. A miracle may 
" be either discovered by men or not. This alters not its 
" essence or its nature. "f 

In order rightly to interpret this definition 
of a miracle, it is necessary to have the author's 
definition of a law of nature, which is given in 
a subsequent part of his essay. 

"It is experience only which gives authority to human 
w testimony ; and it is the same experience which assures us 



* Page 114. 



f Page 462. 



AGAINST MIRACLES. 



123 



" of the laws of nature. When, therefore, these two kinds 
" of experience are contrary, we have nothing to do but 
" subtract the one from the other, and embrace an opinion, 
11 either on one side or the other, with that assurance which 
M arises from the remainder."* 

Having pointed out the difference in our 
definitions, I shall now show a point of resem- 
blance between them, which is apparent in 
the following extract — 

" What we have said of miracles, may be applied without 
" any variation to prophecies ; and indeed all prophecies are 
" real miracles, and as such only can be admitted as proofs 
" of any revelation. "-j- 

The reader who has entered into the rea- 
soning of Chapter VIII. of this fragment will 
perceive that, according to the views there 
maintained, it might be asserted that all mira- 
cles are prophecies : that they are revelations 
more or less in advance of events which, 
although in real accordance, are apparently in 
direct contradiction to the laws of nature. 

* Hume's Essay, vol. ii. p. 129. 

•J* Page 131. A passage in this quotation has for conve- 
nience been marked in italics ; it is not so in the original. 



124 



hume's argument 



Hume's argument in the first part of the 
Essay of Miracles, seems intended to prove that 
although the Deity might cause miracles to be 
worked, yet that it is impossible that those 
who did not witness them, could be convinced 
of their having occurred by any human testi- 
mony. 

In the second part of that essay the author 
applies a limitation to which he requests parti- 
cular attention — namely, that no human testi- 
mony can have such force as to prove a mira- 
cle, and make it a just foundation for any system 
of religion. 

" I beg the limitations here made may be remarked, 
" when I say, that a miracle can never be proved, so as to 
" be the foundation of a system of religion."* 

Had the argument been continued, it might 
have appeared still more startling ; for, as all 
miracles of which we have any account, rest, in 

* Hume's Essay, vol. ii. p. 128. 



AGAINST MIRACLES. 



12) 



the first instance, on the testimony of eye-wit- 
nesses who are not themselves alive to deliver 
their testimony, we require the fact that they 
did so testify, to be confirmed to us by the testi- 
mony of others. Now, if, in order to prove 
the miracle, it must be a greater miracle that 
the testimony of the eye-witnesses is true ; so, 
in order to assure us that the eye-witnesses did 
testify it, it must be a still greater miracle that 
those who assure us of that fact, themselves 
speak the truth. If this second testimony is not 
communicated to us personally, but is again 
transmitted, either through persons or through 
writings, we must again, at each transmission, 
require a greater miracle than at the preceding. 
Thus, it might at first sight be made to appear, 
that the amount of evidence required to esta- 
blish the truth of a miracle, said to have been 
performed at any distant period of past time, 
would be enormous. 

However alarming this doctrine may appear, 
an examination of the real numerical value of 



126 



hume's argument 



the quantities spoken of in Hume's argument as 
greater and less, will prove, as has frequently 
happened in other instances, that the con- 
sequences deduced from it by no means neces- 
sarily follow. 

Hume has deduced the a priori probabi- 
lity against the occurrence of a miracle, from 
the universal experience of mankind; and, 
as it is only our own entire ignorance of all 
their causes which renders the question of mi- 
racles one of probability, there is no objection 
to be made to this step. On the contrary, it 
enables us to lay the foundation of numerical 
deductions, which have none of the vagueness 
of those at which Hume arrived. 

Taking, therefore, Hume's own mode of es- 
timating a miracle, let us suppose the chances 
against its occurrence to be n to 1, where 
n is some enormously large number. Still, 
however, in this view of the question, there is 
a probability, however small, for its occurrence, 



AGAINST MIRACLES. 



127 



whilst there exists an improbability of vast mag- 
nitude against it, It is on this ground that I 
have, according to Hume's own notions, called 
a miracle an improbability ; and we may, there- 
fore, substitute that term for miracle and mi- 
raculous. The argument of Hume, when so 
translated, stands thus : — 

That no testimony is sufficient to establish an 
improbability, unless the testimony be of such a 
kind that its falsehood would be more improba- 
ble than the occurrence of the fact which it en- 
deavours to establish. 

But the " fact which it endeavours to es- 
tablish" is the improbability mentioned in the 
second line. Consequently, the testimony 
must be of such a nature, that its falsehood 
would be more improbable than that first im- 
probability. 

Let us now apply the test of number to the 
argument of Hume ; and, for the sake of simpli- 



128 



hume's argument 



city, let us take the case of the miracle men- 
tioned in the next chapter, and let us assume 
that the improbability that a dead person will 
be restored to life, as deduced from past expe- 
rience, is 200,000,000,000 to 1. 

Let us also suppose that there are witnesses 
who will speak the truth, and who are not them- 
selves deceived in ninety-nine cases out of a 
hundred. Now, let us examine what is the 
probability of the falsehood of a statement in 
which two such persons absolutely unknown 
to and unconnected with each other agree. 

Since the order in which independent wit- 
nesses give their testimony does not affect their 
credit, we may suppose that, in a given num- 
ber of statements, both witnesses tell the truth 
in the ninety-nine first cases, and the false- 
hood in the hundredth. Then, 

The first time the second witness B testifies, 
he will agree with the testimony of the first 



AGAINST MIRACLES. 



129 



witness A, in the ninety-nine first cases, and 
differ from him in the hundredth. Similarly, 
in the second testimony of B, he will again 
agree with A in ninety-nine cases, and differ 
in the hundredth, and so on for ninety-nine 
times ; so that, after A has testified a hundred, 
and B ninety-nine times, we shall have 

99 x 99 cases in which both agree, 

99 cases in which they differ, A being wrong. 

Now, in the hundredth case in which B testi- 
fies, he is wrong ; and, if we combine this with 
the testimony of A, we have ninety-nine cases 
in which A is right and B wrong ; and one case 
only in which both A and B agree in error. The 
whole number of cases, which amounts to ten 
thousand, may be thus divided : — 

99 x 99=9801 cases in which A and B agree in truth, 
1 x 99= 99 cases in which B is true and A false, 

99 X 1= 99 cases in which A is true and B false, 
1x1= 1 case in which both A and B agree in a 

falsehood. 

10,000 cases. 

K 



130 



hume's argument 



As there is only one case in ten thousand 
in which two such independent witnesses can 
agree in error, the probability of their testimony 
being false is ^ or ~ > 

The reader will already perceive how great 
a reliance is due to the concurring testimony 
of two independent witnesses of tolerably good 
character and understanding. It appears that 
the chance of one such witness being in error 
is ; that of two concurring in the same 
error is ^ ; and if the same reasoning be ap- 
plied to three independent witnesses, it will be 
found that the probability of their agreeing in 
error is ; or that the odds are 999,999 to 
1 against the agreement. 

Pursuing the same reasoning, the probability 
of the falsehood of a fact which six such inde- 
pendent witnesses attest is or it is, in 
round numbers, 



AGAINST MIRACLES. 



131 



1,000,000,000,000 to 1 against the falsehood of their tes- 
timony. 

The improbability of the miracle of a dead 
man being restored, is, as we have seen, on the 
principles stated by Hume, 20 * m y> ; or it is — 

200,000,000,000 to 1 against its occurrence. 

It follows, then, that the improbability of the 
falsehood of the concurring testimony of only 
six such independent witnesses, is already five 
times as great as the improbability against the 
miracle of a dead man's being restored to life, 
deduced from Hume's method of estimating 
its probability solely from experience. As the 
argument of Hume is universal, it is sufficient 
for its refutation to give a single instance in 
which it docs not hold. 

The reader will find, in a note in the Ap- 
pendix, the mathematical inquiry, in which, the 
degree of improbability of the miracle and 
k 2 



132 



hume's argument. 



the degree of probability belonging to the wit- 
nesses being assigned, it will be seen whether 
any, and what number of such witnesses, can 
outweigh the improbability of the miracle. 



A PRIORI ARGUMENT. 



133 



CHAP. XI. 

A PiUORI ARGUMENT IN FAVOUR OF THE OCCUR- 
RENCE OF MIRACLES. 

In the present chapter it is proposed to 
prove, that — 

It is more probable that any law, at the know- 
ledge of which we have arrived by observation, 
shall be subject to one of those violations which, 
according to Hume's definition, constitutes a mi- 
racle, than that it should not be so subjected. 

To show the probability of this, we may 
be allowed again to revert to the Calculating 
Engine : and to assume that it is possible to 
set the machine, so that it shall calculate any 



134 



A PRIORI ARGUMENT. 



algebraic law whatever : and also possible so to 
arrange it, that at any periods, however remote, 
the first law shall be interrupted for one or 
more times, and be superseded by any other 
law ; after which the original law shall again 
be produced, and no other deviation shall ever 
take place. 

Now, as all laws, which appear to us regular 
and uniform in their course, and to be subject 
to no exception, can be calculated by the en- 
gine : and as each of these laws may also be 
calculated by the same machine, subject to any 
assigned interruption, at distinct and definite 
periods ; each simple law may be interrupted at 
any point by a portion of any one of all the 
other simple laws : it follows, that the class of 
laws subject to interruption is far more extensive 
than that of laws which are uninterrupted. It 
is, in fact, infinitely more numerous. There- 
fore, the probability of any law with which we 
have become acquainted by observation being 
part of a much more extensive law, and having, 



FOR MIRACLES. 



135 



to use mathematical language, singular points 
or discontinuous functions contained within it, 
is very large. 

Perhaps it may be objected, that the laws 
calculated by such an engine are not laws of 
nature, and that any deviation from laws pro- 
duced by human mechanism does not come 
within Hume's definition of miracles. To this 
it may be answered, that a law of nature has 
been defined by Hume to rest upon experi- 
ence, or repeated observation, just as the truth 
of testimony does. Now, the law produced by 
the engine may be arrived at by precisely the 
same means — namely, repeated observation. 

It may, however, be desirable to explain 
further the nature of that evidence, on which 
the fact, that the engine possesses those powers, 
rests. 

When the Calculating Engine has been set 
to compute the successive terms of any given 



136 



A PRIORI ARGUMENT 



law, which the observer is told will have an 
apparent exception (at, for example, the ten 
million and twenty-third term,) the observer is 
directed to note down the commencement of 
its computations ; and, by comparing these re- 
sults with his own independent calculations of 
the same law, he may verify the accuracy of 
the engine as far as he chooses. It may then 
be demonstrated to him, by the very structure 
of the machine, that if its motion were con- 
tinued, it would, necessarily, at the end of a 
very long time, arrive at the ten-millionth term 
of the law assigned to it ; and that, by an equal 
necessity , it would have passed through all the 
intermediate terms. The inquirer is now de- 
sired to turn on the wheels with his own hand, 
until they are precisely in the same situation 
as they would have been had the engine itself 
gone on continuously, to the ten-millionth 
term. The machine is again put in motion, 
and the observer again finds that each succes- 
sive term it calculates fulfils the original law. 
But, after passing twenty-two terms, he now 



FOR MIRACLES. 



137 



observes one term which does not fulfil the 
original law, but which does coincide with the 
predicted exception. 

The continued movement now again pro- 
duces terms according with the first law, and the 
observer may continue to verify them as long 
as he wishes. It may then be demonstrated to 
him, by the very structure of the machine, that, 
if its motion were continued, it would be impos- 
sible that any other deviation from the appa- 
rent law could ever occur at any future time. 

Such is the evidence to the observer ; and, if 
the superintendent of the engine were, at his 
request, to make it calculate a great variety of 
different laws, each interrupted by special and 
remote exceptions, he would have ample ground 
to believe in the assertion of its director, that 
he could so arrange the engine that any 
law, however complicated, might be calculated 
to any assigned extent, when there should 
arise one apparent exception ; after which the 



138 



A PRIORI ARGUMENT 



original law should continue uninterrupted 
for ever. 

Let us now consider the miracle alluded to by 
Hume — the restoration of a dead man to life. 
According to the definition of that author, our 
belief in such a fact being contrary to the laws 
of nature, arises from our uniform experience 
against it. Our personal experience is small : 
we must therefore have recourse to testimony; 
and from that we learn, that the dead are never 
restored to life ; and, consequently, we have 
the uniform experience of all mankind since 
the creation, against one assigned instance of 
a dead man being so restored. Let us now 
find the numerical amount of this evidence, 
Assuming the origin of the human race to have 
been about six thousand years ago, and taking 
thirty years as the duration of a generation, we 
have — 

6000 

— — = 200 generations. 
30 



FOR MIRACLES. 



139 



And allowing that the average population of 
the earth has been a thousand millions, we 
find that there have been born and have died 
since the creation, 

200 x 1,000,000,000 
=200,000,000,000 individuals. 

Such, then, according to Hume, are the odds 
against the truth of the miracle : that is to say, 
it is found from experience, that it is about two 
hundred thousand millions to one against a 
dead man having been restored to life. 

Let us now compare this with a parallel case 
in the calculations of the engine ; and let us 
suppose the number above stated to be a hun- 
dred million times as great, or that the truth of 
the miracles is opposed by a number of in- 
stances, expressed by twenty places of figures. 

The engine may be set to count the natural 
numbers — 1, 2, 3, 4, &c. ; and it shall continue 



140 



A PRIORI ARGUMENT 



to fulfil that law, not merely for the number of 
times just mentioned, for that number is quite 
insignificant among the vast periods it involves ; 
but the natural numbers shall follow in conti- 
nual succession, until they have reached an 
amount which requires for its expression above 
a hundred million places of figures. If every 
letter in the volume now before the reader's 
eyes were changed into a figure, and if all the 
figures contained in a thousand such volumes 
were arranged in order, the whole together 
would yet fall far short of the vast induction 
the observer would have had in favour of the 
truth of the law of natural numbers. The 
widest range of all the cycles of astronomy and 
geology combined, sink into insignificance be- 
fore such a period. Yet, shall the engine, true 
to the prediction of its director, after the lapse 
of myriads of ages, fulfil its task, and give 
that one, the first and only exception to 
that time-sanctioned law. What would have 
been the chances against the appearance of 
the excepted case, immediately prior to its 



FOR MIRACLES. 



141 



occurrence ? It would have had, according to 
Hume, the evidence of all experience against 
it, with a force myriads of times more strong 
than that against any miracle. 

Now, let the reader, who has fully entered 
into the nature of the argument, ask himself 
this question : — Does he believe that such an 
engine has really been contrived, and what 
reasonable grounds has he for that belief? 

The testimony of any single witness is small 
against such odds ; besides, the witness may 
deceive himself. Whether he speaks truly, will 
be estimated by his moral character — whether 
he deceives himself, will be estimated by his 
intellectual character. The probability that 
such an engine has been contrived, will, how- 
ever, receive great addition, when it is re- 
marked, that mathematical— and, especially, 
geometrical evidence is, of all others, that in 
which the fewest mistakes arise, and in which 
they are most readily discovered ; and when it is 



142 



A PRIORI ARGUMENT. 



added, that the fact of the invention of such an 
engine may be deduced from the drawings 
. with all the force of demonstration, and that it 
rests on precisely the same species of evidence 
as the propositions of Euclid. Whether such an 
engine could be actually made in the present 
state of mechanical art, is a question of quite a 
different order : it must rest upon the opinions 
of those who have had extensive experience in 
that art. The author has not the slightest 
hesitation in stating his opinion to be, that it 
is fully within those limits. 

This, however, is a question foreign to the 
nature of the argument, which might have been 
stated in a more abstract manner, without any 
reference to such an engine. As, however, it 
really arose from that machine, and as visible 
forms make a much deeper impression on the 
mind than any abstract reasonings, it has been 
stated in conjunction with that subject. 



NATURE OF FUTURE PUNISHMENTS. 143 



CHAPTER XII. 



THOUGHTS ON THE NATURE OF FUTURE 
PUNISHMENTS. 



Who has not felt the painful memory of 
departed folly? who has not at times found 
crowding on his recollection, thoughts, feel- 
ings, scenes, by all perhaps but him for- 
gotten, which force themselves involuntarily 
on his attention ? Who has not reproached 
himself with the bitterest regret at the follies 
he has thought, or said, or acted? Time 
brings no alleviation to these periods of morbid 
memory : the weaknesses of our youthful days, 
as well as those of Hter life, come equally 



144 



NATURE OF 



unbidden and unarranged, to mock our atten- 
tion and claim their condemnation from our 
severer judgment. 

It is remarkable that those whom the world 
least accuses, accuse themselves the most ; and 
that a foolish speech,, which at the time of 
its utterance was unobserved as such by all 
who heard it, shall yet remain fixed in the 
memory of him who pronounced it, with a 
tenacity which he vainly seeks to communicate 
to more agreeable subjects of reflection. It is 
also remarkable that whilst our own foibles, 
or our imagined exposure of them to others, 
furnish the most frequent subject of almost 
nightly regret, yet we rarely recall to recollec- 
tion our acts of consideration for the feelings 
of others, or those of kindness and benevolence. 
These are not the familiar friends of our 
memory, ready at all times to enter the domi- 
cile of mind its unbidden but welcome guests. 
When they appear, they are usually summoned 
at the command of reason, from some un- 



FUTURE PUNISHMENTS. 



145 



expected ingratitude, or when the mind retires 
within its council chamber to nerve itself for 
the endurance or the resistance of injustice. 

If such be the pain, the penalty of thought- 
less folly, who shall describe the punishment 
of real guilt ? Make but the offender better, 
and he is already severely punished. Memory, 
that treacherous friend but faithful monitor, 
recalls the existence of the past, to a mind 
now imbued with finer feelings, with sterner 
notions of justice than when it enacted the 
deeds thus punished by their recollection. 

If additional knowledge be given to us, the 
consequences of many of our actions appear in 
a very altered light. We become acquainted 
with many evils they have produced, which, al- 
though quite unintentional on our part, are yet 
a subject of painful regret. But this unavailing 
regret is mixed with another feeling far more 
distressing. We reproach ourselves with not 
having sufficiently employed the faculties we 

L 



146 



NATURE OF 



possessed in acquiring that knowledge, which, 
if we had attained, would have prevented us 
from committing acts we now discover to have 
been injurious to those we best loved. 

On the other hand, the good which such 
increased knowledge enables us to discover 
that we have unintentionally done, fails to pro- 
duce that satisfaction always arising from a vir- 
tuous motive ; and it is accompanied by the 
regret that, by a sufficient cultivation of our 
faculties, we might have enjoyed a still higher 
satisfaction, by a more efficient service to our 
fellow-creatures. 

Thus, on whichsoever side we look at the 
question, knowledge alone is advantageous 
to virtue ; and if additional knowledge alone 
were given in a future life, it would cause the 
best of us to regret the errors of the present. 

Let us now consider the consequences of a 
higher tone of moral feeling— of a perception 



FUTURE PUNISHAIENTS. 



147 



of excellencies of character, hitherto unap- 
preciated. 

Without the torment arising from additional 
knowledge, we may, in such circumstances, 
perceive, that the pain we have inflicted for 
imagined offences was quite beyond their real 
deserts ; and we may feel that the justice we 
have done to others, has been quite dispropor- 
tioned to the sacrifices they have made to 
serve us. 

If, without any addition to our intellectual 
faculties, increased perfection were given to 
our bodily senses, the same result would ensue. 
Wollaston has shown, that there are sounds of 
such a nature, that they can be heard by some 
individuals, but are inaudible to others, — a cir- 
cumstance which may arise either from the 
incapacity of the parts of the ear to vibrate in 
the same time as those which produced the 
sound, or from the force of the sounding body 
being insufficient to communicate through the 
l 2 



148 



NATURE OF 



air motion to those portions of the ear required 
for the production of the sensation of hearing. 

If we imagine the soul in an after stage of our 
existence, connected with a bodily organ of 
hearing so sensitive, as to vibrate with motions 
of the air, even of infinitesimal force, and if it 
be still within the precincts of its ancient abode, 
all the accumulated words pronounced from 
the creation of mankind, will fall at once on 
that ear. Imagine, in addition, a power of 
directing the attention of that organ entirely 
to any one class of those vibrations : then will 
the apparent confusion vanish at once ; and 
the punished offender may hear still vibrating 
on his ear the very words uttered, perhaps, 
thousands of centuries before, which at once 
caused and registered his own condemnation. 

It seems, then, that with improved faculties 
or increased knowledge, we could scarcely 
look back with any satisfaction on our past lives 
— that, to the major part of our race, oblivion 



FUTURE PUNISHMENTS. 



149 



would be the greatest boon. If, however, in a 
future state, we could turn from the contem- 
plation of our own imperfections, and with in- 
creased knowledge apply our minds to the 
discovery of nature's laws, and to the invention 
of new methods by which our faculties might 
be aided in that research, pleasure the most 
unalloyed would await us at every stage of 
our progress. 

Unclogged by the dull corporeal load of mat- 
ter which tyrannizes even over our most intel- 
lectual moments, and chains the ardent spirit 
to its unkindred clay, we should advance in the 
pursuit, stimulated instead of wearied by our 
past exertions, and encountering each new dif- 
ficulty in the inquiry, with the accumulated 
power derived from the experience of the past, 
and the irresistible efforts resulting from the 
confidence of ultimate success. 

Whether, then, we regard our future pros- 
pects as connected with afar higheracuteness of 



150 NATURE OF FUTURE PUNISHMENTS. 

our present senses — or, as purified by more 
exalted moral feelings — or, as guided by in- 
tellectual power, surpassing all we contem- 
plate on earth, we equally arrive at the conclu- 
sion, that the mere employment of such enlarged 
faculties, in surveying our past existence, will 
be an ample punishment for all our errors ; 
whilst, on the other hand, if that Being who 
assigned to us those faculties, should turn their 
application from the survey of the past, to the 
inquiry into the present and to the search 
into the future, the most enduring happiness 
will arise from the most inexhaustible source. 



ON FREE WILL. 



151 



CHAP. XIII. 

REFLECTIONS ON FREE WILL. 

The great question of the incompatibility of 
one of the attributes of the Creator — that of 
fore-knowledge, with the existence of the free 
exercise of their will in the beings he has 
created, — has long baffled human comprehen- 
sion ; nor is it the object of this chapter to 
enter upon that difficult question. 

As, however, some of the properties of the 
Calculating Engine seem, although but very 
remotely, to bear on a similar question, with 
respect to finite beings, it may, perhaps, not 
be entirely useless to state them. 



152 



REFLECTIONS 



It has already been observed, that it is pos- 
sible so to adjust the engine, that it shall change 
the law it is calculating into another law at 
any distant period that may be assigned. 

Now, by a similar adjustment, this change 
may be made to take place at a time not fore- 
seen by the person employing the engine. For 
example : when calculating a table of squares, 
it may be made to change into a table of cubes, 
the first time the square number ends in the 
figures — 

269696 ; 

an event which only occurs at the 99736th 
calculation ; and whether that fact is known to 
the person who adjusts the machine or not, is 
immaterial to the result. 

But the very condition on which the change 
depends, maybe impossible. Thus, the change 
of the law from that of squares to that of 
cubes may be made to take place the first time 



ON FREE WILL. 



153 



the square number ends with a 7. But it is 
known, that no square number can end in a 
7 ; consequently the event, on the happening 
of which the change is determined, can itself 
never take place. Yet, the engine retains 
impressed on it a law, which would be called 
into action if the event on which it depends 
could occur in the course of the law it is cal- 
culating. 

Nay, further, if the observer of the engine 
is informed, that at certain times he can move 
the last figure the engine has calculated, and 
change it into any other, in consequence of 
which it becomes possible that some future 
term may end in 7 ; then, after he has so 
changed the last figure, whenever that ter- 
minal figure arrives, all future numbers calcu- 
lated by the machine will follow the law of the 
cubes. 



154 



REFLECTIONS 



These contingent changes may be limited to 
single exceptions, and the arrival of such ex- 
ception may be made contingent on a change 
which is only possible at certain rare periods. 
For example : the engine may be set to calculate 
square numbers, and after a certain number of 
calculations — ten million and fifty-three, for 
example, it shall be possible to add unity to a 
wheel in another part of the engine, which in 
every other instance is immovable. This fact 
being communicated to the observer, he may 
either make that addition or refrain from it : 
if he refrain, the law of the squares will con- 
tinue for ever ; if he make the addition, one 
single cube will be substituted for that square 
number, which ought to occur ten million and 
five terms beyond the point at which he made 



ON FREE WILL. 



155 



the addition ; and after that no future addi- 
tion will ever become possible, and no future 
deviation from the law of the squares will 
ever occur. 



156 



THE ORIGIN OF EVIL. 



CHAP. XIV. 

THOUGHTS ON THE ORIGIN OF EVIL. 



/ had intended to have put into writing the 
substance of an interesting discussion I once 
had with a distinguished Philosopher, now no 
more, but other demands on my time have pre- 
vented the completion of this intention. 



CONCLUSION. 



157 



CONCLUSION. 



Reader, I have now fulfilled the task I under- 
took. Labouring under that imputed mental 
incapacity which the science I cultivate has 
been stated to produce, I have brought from 
the recesses of that science the reasonings and 
illustrations by which I have endeavoured 
faintly to embody the human conception of the 
Almighty mind. It is for you to determine 
whether the trains of thought I have excited 
have lowered or exalted your previous notions 
of the power and the knowledge of the 
Creator. 



158 



CONCLUSION. 



That prejudice which I have endeavoured to 
expose is not a merely speculative opinion, it 
is a practical evil ; and those whose writings have 
been supposed to give support to it, will, I am 
sure, feel grieved when they learn that it is 
used by the ignorant and the designing, for the 
injury of the virtuous and the instructed; that 
it is employed as a firebrand, to disturb the re- 
lations of social life. They will also, if the 
arguments I have used have the same weight 
on their minds which they have had on my 
own, lament still more deeply that they should 
have contributed, in any degree, to throw 
discredit on that species of knowledge which 
is now found to supply some of the strongest 
arguments in favour of religion. I will, how- 
ever, hope that the opinions I have com- 
bated are not shared or even countenanced 
by the higher authorities of our Protestant 
Church ; and I cannot better conclude this 
Fragment, than by recalling to the reader the 
words of one, whose power of reasoning, and 
whose love of truth, add dignity to the high 
station he so deservedly fills : — 



CONCLUSION. 



159 



" Lastly, As we must not dare to withhold 
" or disguise revealed religious truth, so, we 
u must dread the progress of no other truth. 
" We must not imitate the bigoted Romanists 
u who imprisoned Galileo ; and step forward 
" Bible in hand (like the profane Israelites car- 
" rying the Ark of God into the field of battle) 
<f to check the inquiries of the Geologist, the 
" Astronomer, or the Political-economist, from 
u an apprehension that the cause of religion 
u can be endangered by them.* Any theory 
" on whatever subject, that is really sound, can 
" never be inimical to a religion founded on 
" truth ; and any that is unsound may be re- 
" futed by arguments drawn from observation 
" and experiment, without calling in the aid of 
" revelation. If we give way to a dread of 
" danger from the inculcation of any scriptural 
" doctrine, or from the progress of physical or 
" moral science, we manifest a want of faith in 
" God's power, or in his will, to maintain his 



See First Lecture on Political Economy. 



160 



CONCLUSION. 



" own cause. That we shall indeed best fur- 
" ther his cause by fearless perseverance in an 
" open and straight course, I am firmly per- 
" suaded ; but it is not only when we perceive 
" the mischiefs of falsehood and disguise, and 
" the beneficial tendency of fairness and can- 
" dour, that we are to be followers of truth : 
u the trial of our faith is, when we cannot per- 
" ceive this : and the part of a lover of truth 
" is to follow her at all seeming hazards, after 
" the example of Him who ' came into the 
" world that He might bear witness to the 
" Truth/"* 

* Sermons by the Archbishop of Dublin. 



APPENDIX. 



M 



APPENDIX. 



NOTE A. 



ON THE GREAT LAW WHICH REGULATES MATTER. 

Ever since the period when Newton established the 
great law of gravity, philosophers have occasionally 
speculated on the existence of some more comprehen- 
sive law, of which gravity itself is the consequence. 
Although some have considered it vain to search for a 
more general law, the great philosopher himself left 
encouragement to future inquirers ; and the time, per- 
haps, has even now arrived, when such a discovery may 
be near its maturity. It would occupy too much space 
to introduce many illustrations of this opinion ; there 
is, however, one which deserves attention, because it is 
not merely a happy conjecture, but the hypothesis on 
which it rests has been carried by its author, through 
the aid of profound mathematical reasoning, to many 
of its remote consequences. 

m 2 



164 



APPENDIX. 



M. Mosotti* has shown, that by supposing matter 
to consist of two sorts of particles, each of which repels 
similar particles, directly as the mass, and inversely as 
the squares, of their distances ; whilst each attracts those 
of the other kind, also according to the same law, — 
then the resulting attractions explain all the pheno- 
mena of electricity, and there remains a residual force, 
acting at all sensible distances, according to the law of 
gravity. 

Many of the discoveries of the present day point 
towards a more general law ; and many of the philo- 
sophers of the present time anticipate its near approach. 
Under these circumstances, it may be interesting as 
well as useful briefly to state the principles which such 
a law must comprehend ; and to indicate, however im- 
perfectly, the path to be pursued in the research. 

If matter be supposed to consist of two sorts of 
particles, or rather, perhaps, of two sorts of centres of 
force, of different orders of density ; and if the parti- 
cles of each order repel their own particles, according 
to a given law, but attract particles of the other kind, 
according to another law, — then, if we conceive only 
one particle of the denser kind to exist, and an infinite 

* Professor of Physics at the University of the Ionian Islands. — 
The paper of M. Mosotti has heen translated, and published by Mr. 
R. Taylor, in the third number of the Scientific Memoirs ; a work 
which it is proposed shall contain translations of all the most important 
original papers printed in foreign countries. 



APPENDIX. 



165 



number of the other kind, that single particle will be- 
come the centre of a system, surrounded by all the 
others, which will form around it an atmosphere denser 
near the central body. 

If we conceive a stream of particles, similar to those 
forming the atmosphere, to impinge upon it, so as just 
to overcome its resistance, they will, whilst continually 
producing undulations throughout its whole extent, 
gradually increase its magnitude, until it attains such a 
size, that the repulsion of the particles at its outer sur- 
face is just balanced by the attraction of the central 
particle. If the stream continue after this point is 
reached, the whole outer layer will be pressed a little 
beyond the limit of attraction, and will fly off at right 
angles to the surface, which might then be said to 
radiate. 

If the whole of the space in which such a central 
particle with its atmosphere is placed, is itself full of 
atmospheric particles, then their density will increase 
in approaching the central body; and if a stream of 
such particles were directed towards the centre, they 
might produce throughout the atmosphere vibrations, 
which would be transmitted from it in all directions. 

If two such central particles, with their atmospheres, 
exist at a distance from each other, they will be drawn 
together by a force depending on the difference between 



166 



APPENDIX. 



the mutual repulsion of their atmospheres and central 
bodies respectively for each other, and the attraction of 
each central particle for its neighbour's atmosphere : and 
in order to coincide with the existing law of nature, 
this must be directly as the mass, and inversely as the 
square, of the distance. The other conditions which 
such a law must satisfy, are— 

1. That the juxtaposition of such atoms must, in 
some circumstances, form a solid body. 

2. In other circumstances, a fluid. 

3. That again, in still other circumstances, its par- 
ticles shall repel each other, or the body become 
gaseous. 

4. In the first state the body must possess cohesion, 
tenacity, malleability, elasticity ; the measure and extent 
of each of which must result generally from the origi- 
nal law, and in each particular case from the constants 
belonging to the substance itself. 

5. In the second, it must possess capillarity, suscep- 
tibility of being compressed without becoming solid, 
as also elasticity. 

But besides these, the central atoms must admit of a 
more intimate approach, so that their atmospheres may 



APPENDIX. 



167 



unite and form one atmosphere. This might constitute 
chemical union. Binary compounds might then (sup- 
posing the distance between the two central particles to 
be very small, compared with the diameters of the at- 
mospheres) have atmospheres not quite spherical, and 
attracting differently in different directions ; thus pos- 
sessing polarity. Combinations of three or more 
atoms, as the central body of one atmosphere, might 
give great varieties of attractive forces. Each dif- 
ferent combination would give a different atmosphere ; 
and the equation of its surface might, perhaps, be- 
come the mathematical expression of the substance 
it constituted. Thus, all the phenomena produced by 
bodies, acting chemically on each other, might be de- 
duced from the comparison of the characteristic surfaces 
of the atmospheres of their atoms. Another result, also, 
might ensue. Two or more central atoms uniting, 
might either not be able to retain the same amount of 
atmosphere, or they might possibly be able to retain a 
larger quantity. If the particles of such atmospheres 
constituted heat, it would in the former case be given 
out, and in the latter absorbed by chemical union. 

Hence the whole of chemistry, and with it crystal- 
lography, would become a branch of mathematical 
analysis, which, like astronomy, taking its constants 
from observation, would enable us to predict the cha- 
racter of any new compound, and possibly indicate the 
source from which its formation might be anticipated. 



168 



APPENDIX. 



For the sake of simplicity, two species of particles 
only have been mentioned above ; but it seems more 
probable, that matter consists of at least three kinds. 

Suppose each kind to repel its own particles ; and 
supposing the central atom, whilst it repels similar 
particles, to attract those of the two other kinds ; and 
moreover, that these latter were either repulsive, or 
indifferent to each other. We might then conceive 
matter to be made up of particles, each having a central 
point, with an atmosphere surrounding it, and this at- 
mosphere again inclosed within another and larger one. 

Under such circumstances, the outer atmosphere 
might give rise to heat and light, to solidity and fluidity, 
and the gaseous condition ; to capillarity, to elasticity, 
tenacity, and malleability. The more intimate union 
of the central atoms, by which two or more become 
enclosed in one common atmosphere of the second 
kind, might represent chemical combinations, and per- 
haps that atmosphere itself be electricity. Possibly, 
also, this intermediate atmosphere, acted on by the 
pressure of the external one, and by the attraction of 
the central atom, might take the liquid form. These 
binary or multiple-combinations of the original atoms, 
and their smaller atmospheres, would still be enclosed 
in an atmosphere of the outer kind, which might be 
nearly spherical. The joint action of the three might, 
at sensible distances, produce gravity. 



APPENDIX. 



169 



The reader should, however, bear in mind, that 
these hints are but thrown out as objects of reflection 
and inquiry ; and that nothing but a profound mathe- 
matical investigation can establish them, or even give 
to them that temporary value which arises from any 
hypothesis, representing a large collection of facts. 



170 



APPENDIX. 



NOTE B. 



ON THE CALCULATING ENGINE. 

The nature of the arguments advanced in this volume 
having obliged me to refer, more frequently than I 
should have chosen, to the Calculating Engine, it be- 
comes necessary to give the reader some brief account 
of its progress and present state. 

About the year 1821, I undertook to superintend, 
for the Government, the construction of an engine for 
calculating and printing mathematical and astronomical 
tables. Early in the year 1883, a small portion of the 
machine was put together, and it performed its work 
with all the precision which had been anticipated. At 
that period circumstances, which I could not control, 
caused what I then considered a temporary suspen- 
sion of its progress ; and the Government, on whose 



APPENDIX. 



171 



decision the continuance or discontinuance of the work 
depended, have not yet communicated to me their 
wishes on the question. The first illustration I have 
employed is derived from the calculations made by 
this engine. 

About October, 1834, I commenced the design of 
another, and far more powerful engine. Many of the 
contrivances necessary for its performance have since 
been discussed and drawn according to various prin- 
ciples ; and all of them have been invented in more 
than one form. I consider them, even in their pre- 
sent state, as susceptible of practical execution ; but 
time, thought, and expense, will probably improve 
them. As the remaining illustrations are all drawn 
from the powers of this new engine, it may be right to 
state, that it will calculate the numerical value of any 
algebraical function — that, at any period previously 
fixed upon, or contingent on certain events, it will cease 
to tabulate that algebraic function, and commence the 
calculation of a different one, and that these changes 
may be repeated to any extent. 

The former engine could employ about 120 figures 
in its calculations ; the present is intended to compute 
with about 4,000. 

Here I should willingly have left the subject ; but 
the public having erroneously imagined, that the sums 



172 



APPENDIX. 



of money paid to the workmen for the construction of 
the engine, were the remuneration of my own services, 
for inventing and directing its progress ; and a Com- 
mittee of the House of Commons having incidentally 
led the public to believe that a sum of money was voted 
to me for that purpose, I think it right to give to that 
report the most direct and unequivocal contradiction. 



APPENDIX. 



178 



NOTE C. 

EXTRACT FROM THE THEORY OF PROBABILITIES OF 
LAPLACE. 

" Nous devons done envisager l'etat present de l'uni- 
vers, comme l'effet de son etat anterieur, et comrae la 
cause de celui qui va suivre. 

" Une intelligence qui pour un instant donnee, con- 
naitrait toutes les forces dont la nature est animee, et 
la situation respective des etres qui la composent, si 
d'ailleurs elle etait assez vaste pour soumettre ces don- 
nees a l'anaiyse, embrasserait, dans la merae formule, 
les mouvemens des plus grands corps de l'univers et ceux 
du plus leger atome : rien ne serait incertain pour elle, 
et l'avenir, comme le passe, serait present a ses yeux. 
L'esprit humain oifre, dans la perfection qu'il a su don- 
ner a rastronomie, une faible esquisse de cette intelli- 



174 



APPENDIX. 



gence. Ses decouvertes en mecanique et en geometrie, 
jointes a celle de la pesanteur universelle, 1'ont mis a 
portee de comprendre dans les memes expressions ana- 
lytiques, les etats passes et futurs du systeme du 
monde. 

" En appliquantle meme methode a quelques autres 
objets de ses connaissances, il est parvenu a ramener 
a des lois generates, les phenomenes observes, et a 
prevoir ceux que des circonstances donnees doivent 
faire eclore. Tous ses efforts dans la recherche de la 
verite, tendent a le rapprocher sans cesse l'intelligence 
que nous venons de concevoir, mais dont il restera 
toujours infiniment eloigne. Cette tendance propre a 
l'espece humaine, est ce qui la rend superieure aux 
animaux ; et ses progres en ce genre, distinguent les 
nations et les siecles, etfondent leur veritable gloire." — 
Laplace, Theorie Analytique des Probability. 



APPENDIX 



17.5 



NOTE D, 



NOTE TO CHAP. VIII. ON MIRACLES. 

The view taken of miracles in Chapter VIII. is the 
same as that contained in the work of Butler, on the 
Analogy of Religion to the Constitution and Course 
of Nature. Inquiries connected with the Calculating 
Engine, impressed it very forcibly on my own mind, 
and I have drawn the illustrations chiefly from that 
subject. I cannot, however, forbear referring the 
reader to the opinion of Sir J. Herschel, expressed at 
the beginning of his letter to Mr. Lyell, (see Note I.) 
because it confirms me in the belief, that the more pro- 
foundly we inquire into the mechanism of nature, the 
more certainly we arrive at that conclusion. 



176 



APPENDIX. 



NOTE E. 

NOTE TO CHAPTER X. ON HUME'S ARGUMENT 
AGAINST MIRACLES. 

The example in the text is sufficient to show that 
the conclusion at which Hume arrived respecting the 
sufficiency of testimony to support a miracle, will not 
bear the test of a numerical examination. It may, 
however, be interesting to point out the amount of tes- 
timony required, under different circumstances. 

The reader will observe, that throughout the chapter 
to which this note refers, as well as in the note itself, 
the argument of Hume is taken strictly according to 
his own interpretation of the terms he uses, and the 
calculations are founded on them ; so that it is from 
the very argument itself, when fairly pursued to its 
full extent, that the refutation results. 



APPENDIX, 



177 



Both our belief in the truth of human testimony, 
and our belief in the permanence of the laws of nature, 
are, according to Hume, founded on experience ; we 
may, therefore, in the complete ignorance in which he 
assumes we are, with respect to the causes of either, 
treat the question as one of the probability of an event 
deduced solely from observations of the past. 

If an event has been observed to happen m times in 
succession, it is known that the probability of its hap- 
pening the next time is m 1 , and the probability of 
m + 2 

its not arriving is •* If we suppose m to repre- 

sent the amount of the uniform experience of all 
mankind, from the creation to the present time, it will 

be a very large number, and — will represent the 

probability of the occurrence of a miracle opposed to 
that experience. 

Again: if it is found from experience, that a certain 
class of men out of every p statements, make one of 
them false, either from ignorance or design, then the 



• " On trouve ainsi qu'un cvenement etant arrive de suite, un 
nombre quelconque de fois; la probability qu'il arrivera encore la 
fois suivante est egale a ce nombre augment^ de l'unite, divise par 
le mCme nombre augmente* de deux unites." — Laplace s Tk&nrU Aim- 
lytiquc dcs Proba/>ili/cs, p. xiii. 

M 



178 



APPENDIX. 



probability of the falsehood of a statement made by 



The probability that two such persons will concur 



Now, according to Hume 1 s argument, the falsehood 
of the testimony by which a miracle is supported, must 

be a more miraculous event than the occurrence of the 
miracle itself. 

Here, then, we have for the measure of the improba- 
bility of the testimony -~ , and for that of the occur- 
rence of the miracle — ^—7. ; and, in order to prove 
m + 2 r 

the miracle, the first improbability must be greater 
than the second. But this can only happen when 
p n ^>m + 2. 
Hence, n log. p ^> log. (in + 2) 



such a person, is 



1 



in falsehood, is ] 




and n^> 



log. (m + 2) 
log.p 



It follows, therefore, that however large m may be, 
or however great the quantity of experience against the 



APPENDIX. 



179 



occurrence of a miracle, (provided only that there are 
persons whose statements are more frequently cor- 
rect than incorrect, and who give their testimony in 
favour of it without collusion,) a certain number n can 
always be found; so that it shall be a greater im- 
probability that they shall agree in erro?% than that the 
miracle shall occur. 

Let us suppose each of the witnesses who gives 
independent testimony, makes one erroneous state- 
ment in ten; then 

v log. (m + 2) ^ , , _ N 

And, moreover, let us suppose the number of places 
of figures contained in m + 2, to be Jc ; then log. (m + 2) 
is nearly equal to k — 1 , and 

n>k- h 

Now let the number of observed instances in which 
the miracle has not occurred be a million million ; 

or, 1,000,000,000,000, 

then the number of such witnesses necessary to prove 
its occurrence is 

rc>log.(10'-'+2)>12, 

or thirteen such witnesses are sufficient. 

If p = 100, then we must have for the number 
of such witnesses, 

N 2 



180 



APPENDIX. 



^ log, (m + 2) ^ l og, (m + 2) 
^ log. 100 ^ 2 

and if, as before, m is a million millions, 

«> l0 ^P^>\?>e, 

or seven witnesses, are sufficient. 

It may be proper to remark, that if a person has 
established his power to work a miracle in one or more 
instances, the probability of his being able to do so in 
any other case becomes considerable, whatever may be 
the probability of his usual statements. For, as we have 
observed that in the one or more instances in which 
he stated that he should perform a miracle, the event 
followed his prediction ; and, also, that in no instance 
it failed to follow such prediction : we must treat the 
case in the same manner as the occurrence of an event 
m times in succession ; and, if he have performed m 
miracles, the probability that he will perform any other 
which he predicts is m _j_ \ 
m + 2' 

or, if he has performed a miracle only once, it is two 
to one that he has power to perform the next miracle 
he predicts. 

The view explained in the chapter of the text to 
which this note refers, was taken previously to my pe- 
rusal of the observations of Dr. Chalmers " on the 



APPENDIX. 



181 



power which lies in the concurrence of distinct testi- 
monies,"* contained in a work pointed out to me by 
a friend to whom I had mentioned the subject. Dr. 
Chalmers' view is, I believe, substantially the same as 
my own, as far as relates to the effect of concurrent 
testimony ; and had the nature of his work admitted 
the introduction of algebraic operations, he would, 
most probably, have combined it with the other 
principle I have employed, of the probability of the 
occurrence of a future event from observations of the 
past, and thus have arrived at the complete answer to 
the argument of Hume against miracles, by not only 
showing the possibility of supporting them by testi- 
mony, but even of ascertaining, in any given circum- 
stances, the precise number of witnesses required. 

* Evidences of the Christian Revelation, vol i. p. 129. 



182 



APPENDIX. 



NOTE F. 



ON THE CONSEQUENCES OF CENTRAL HEAT* 

The increase of temperature observed as we descend 
below the earth's surface, as well as other pheno- 
mena, have led to a very general opinion, that great 
heat exists in the interior of the earth, and that the 
body of our planet, having been at one time intensely 
heated, has cooled down to its present temperature. 
With the view of pointing out courses of inquiry, by 
which these opinions may ultimately be tested by ob- 
servation, it is expedient to take a cursory view of 
some of the consequences of such an hypothesis. 

And first, let us imagine the exterior of our globe to 
have once been in a state of intense heat. No fluid 
such as water could then have existed on its surface : 
it would instantly have been converted into vapour ; and 



APPENDIX. 



1S3 



notwithstanding the increased weight of atmosphere 
thus produced, and pressing on its surface, sufficient 
heat would have reduced all fluids to the gaseous state. 
Let us, however, inquire as to the possible extent of 
such an atmosphere. 

In the first place, it could not extend beyond that 
point at which the moon's attraction is equal to that 
of the earth. In the next place, much more con- 
tracted limits would be prescribed by the effect of 
centrifugal force, and of the cooling of the vapour by 
expansion, and by its distance from the source of ra- 
diant heat, which had produced that state. 

It would be interesting to inquire, what would be 
the nature of the surface of the atmosphere under such 
circumstances. At the distance at which the centrifugal 
force is equal to that of gravity, it might happen that 
the temperature was scarcely sufficient to maintain the 
water in a gaseous state. Should this have been the 
case, a belt of perpetual clouds might have been formed, 
resembling those of Jupiter. 

If, at this limit, a still lower degree of temperature 
prevailed, instead of a belt of clouds, a ring of ice 
might be formed. 

This ring of ice, being exposed to different effects of 
radiation from various parts of the earth's surfac f, 



APPENDIX. 



might, by the superior heat at one part, become di- 
minished, whilst the condensation of vapours might 
augment less exposed parts : and these conditions 
might continue, until at last the ring itself was melted 
through at one point, and the whole would fall down 
on the surface of the planet. The tearing up of that 
surface from such an event, would be augmented by 
the sudden conversion of the solid ice into steam ; and 
after a time, the fragments of the ring would be ab- 
sorbed again into the atmosphere of the planet. 

Let us now suppose, owing to the gradual cooling 
down of the whole globe, the limit of condensation of 
steam into water, to occur at a nearer point than that at 
which the centrifugal force equals that of gravity. As 
soon as the steam is condensed into water, it will de- 
scend towards the surface of the earth ; but that surface 
being still very hot, will, by its radiation, again con- 
vert the descending shower into steam ; and this will 
happen at different heights above the surface, accord- 
ing to the radiating power of the part below. We 
may, therefore, conceive a shell surrounding the earth, 
the outer surface of which has just been condensed into 
water, and the inner consists of vapour, just re-con- 
verted into that state by the earth's radiation. These 
surfaces will attain different heights in different places. 
Between these two surfaces there will exist a perpetual 
rain, descending from the upper as a gentle shower, 
becoming gradually a violent current, and then as 



APPENDIX . 



185 



it falls re-absorbed into another gentle shower, which 
is entirely absorbed in approaching the heated surface. 

Such being the state of things, let us imagine the 
globe to cool down uniformly. The lower surface of 
the descending rain, which is placed at irregular 
heights, will at length be brought down to the earth's 
surface in one or more points. The effect of this, which 
will in the first instance be a gentle shower, would be 
to cool that portion of the surface on which it foils, and 
hence to diminish its radiating power. This change, in 
its turn, will lower the under surface of the watery shell, 
so that a more violent rain, and ultimately an impetuous 
torrent will continue, perhaps, for thousands of years, 
its uninterrupted vertical action on the surface exposed 
to its force. The excavation of the largest valleys, or 
even of ocean beds, is not too much to expect from 
such forces. 

But let us take another view of the consequences of 
such an original state of incandescence. The whole of 
the fluids now on the surface of the earth must then 
have been suspended in its atmosphere. But the ex- 
tent of that atmosphere is itself limited by various 
causes : the attraction of other bodies, the effects of 
centrifugal force, the decrease of temperature, and the 
distances at which the particles of gaseous bodies cease 
to repel each other, all have their influence in deter- 
mining its form and magnitude. Let us suppose that 
we possessed data from which the approximate amount 



186 



APPENDIX. 



of vapour contained in the entire atmosphere were 
known, and consequently the whole amount of water 
in it ; then, since we know the area of the present seas, 
we might easily ascertain their average depth. If the 
result of such a computation should give a mean depth 
much less than that which we know the ocean to pos- 
sess, — as, for instance, only a hundred feet, — then we 
might conclude, either that the surface of the earth had 
never been in such a state of incandescence as has been 
supposed, or that if it had, that a new source of aqueous 
vapour had been supplied to it, subsequently to its 
cooling down. 



APPENDIX. 



187 



NOTE G. 

ON THE ACTION OF EXISTING CAUSES IN PRODUCING 
ELEVATIONS AND SUBSIDENCES IN PORTIONS OF 
THE EARTH'S SURFACE. 

The following explanation of the origin of many of 
the changes at present going on on the earth's surface, 
was suggested in endeavouring to account for the very 
singular phenomena presented by the temple of Jupiter 
Serapis, at Puzzuoli, near Naples. The facts relat- 
ing to that temple were stated in a paper presented to 
the Geological Society of London, in March, 1834 ; 
an abstract of which was published shortly after. 

The following positions are taken as the basis of the 
reasoning on this subject : — 

1. That, as we descend below the surface of the 
earth, the temperature increases. 



188 



APPENDIX. 



2. That solid rocks expand by being heated ; but 
that clay, and some other substances, contract under 
the same circumstances. 

S. That different rocks and strata conduct heat 
differently. 

4. That the earth radiates heat differently, at dif- 
ferent parts of its surface, according as it is covered 
with forests, with mountains, with deserts, or with water. 

5. That existing atmospheric agents, and other 
causes, are constantly changing the condition of the 
surface of the globe. 

The only one of these propositions on which, in the 
present state of knowledge, the slightest question can be 
raised, is the first. But the observations on which it 
depends have latterly become so numerous, that the 
general fact of an increase of temperature, on descend- 
ing into the crust of the earth, can scarcely be ques- 
tioned ; although the exact law of this increase, and 
the extent to which it penetrates, are yet undecided. 

An increase of 1° Fahrenheit's thermometer, for every 
50 or 60 feet we penetrate below the earth's surface, 
seems nearly the average result of observations. If the 
rate continue, it is obvious that, at a small distance below 
the earth's surface, we shall arrive at a heat which will 



No. 1. 




APPENDIX. 



191 



keep all substances with which we are acquainted in a 
state of fusion. Without, however, assuming the 
fluidity of the central nucleus, — a question yet unsettled, 
and which rests on very inferior evidence* to that by 
which the principles here employed are supported, — we 
may yet arrive at important conclusions ; and these may 
be applied to the case of central fluidity, according to 
the opinions of the inquirer. 

If we consider the temperature of any point: — for 
example, G, situated two miles below the surface of 
an elevated table land, A, in the annexed wood-cut ; 
and if we imagine a surface passing through all the 
points of equal temperature ; then, as this surface passes 
under the adjacent ocean, which we may suppose, on an 
average, to be two miles deep, it is evident that the 
surface of equal heat will descend towards the earth's 
centre ; because, if it did not, we should have great heat 
nearly in contact with the bottom of the sea. In the first 
figure, B is the surface of the ocean. A D, the sur- 
face of the land, and of the bed of the ocean. The 
broken line, G F, is the isothermal line. Let us now 
suppose, by the continual wearing down of the conti- 
nents and islands adjoining this ocean, that it becomes 
nearly filled up. The broken line C, in the second 
figure of the wood-cut, indicates the new bottom. The 

* The reader will find this question fully discussed in the 17th 
chapter of Lyell's Geology ; On the Causes of Earthquakes and 
Volcanos. 



192 



APPENDIX. 



former bottom of the ocean being now covered with a 
bad conductor of heat, instead of with a fluid which 
rapidly conveyed it away, the surface of uniform tem- 
perature will rise, slowly but considerably, as is shown 
at G E, in the third figure. In the fourth figure, the 
first bed of the ocean, A D, and its isothermal line, 
G F, as well as the new bed, A C, of the ocean, and its 
corresponding isothermal line, G E, are all shown at 
one view. 

The newly formed strata will be consolidated by 
the application of heat; they may, perhaps, contract 
in bulk, and thus give space for new deposits, which 
will, in their turn, become similarly consolidated. 
But the surface of uniform temperature below the 
bed of that ocean cannot rise towards the earth's 
surface, without an increase in the temperature of all 
the beds of various rock on which it rests ; and this 
increase must take place for a considerable depth. 
The consequence of this must be a gradual rise of 
the ancient bed of the ocean, and of all the de- 
posits newly formed upon it. The shallowness of 
this altered ocean will, by exposing it to greater evapo- 
ration from the effect of the sun's heat, give increased 
force to the atmospheric causes still operating, to fill 
it up. 

Possibly the conducting power of the heated rocks 
may be so slow, that its total effect may not take place 



APPENDIX. 



193 



for centuries after the sea has given place to dry land ; 
and we can conceive, in such circumstances, the force of 
the sun's rays acting on the surface, and the increasing 
heat from below so consolidating that surface, that it may 
again descend below the level of adjacent seas, even 
though its first bottom is still subject to the elevatory 
process. Thus, a series of shallow seas or large lakes 
might be formed ; and these processes might even be 
repeated several times, before the full effect of the ex- 
pansion from below had permanently raised the whole 
newly-formed land above the effects of the adjacent seas. 

If the sea were originally much deeper, or, if in 
particular parts it were much deeper, as, for in- 
stance, ten or twenty miles, then such portion might, 
after the lapse of many ages, acquire a red, or even a 
melting heat, and the conversion into gases of some 
of the substances thus operated on, might give rise to 
earthquakes, or to subterraneous volcanoes. 

On the other hand, as the high land gradually wears 
away, by the removal of a portion of its thickness, and 
as the cooling down of its surface takes place, its con- 
traction might give rise to enormous rents. If these 
cracks penetrate to any great reservoirs of melted mat- 
ter, such as appear to subsist beneath volcanos, then 
they will be compressed by the contraction, and the 
melted matter will rise and fill the cracks, which, when 
cooled down, will become dykes. 

6 



194 APPENDIX. 

If these rents do not reach the reservoir of melted 
matter, and if there exist in the neighbourhood any 
volcanic vents connected with it, the contraction of 
the upper strata may give rise to volcanic eruptions, 
through those vents, which might be driven by such 
a force to almost any height. These eruptions may 
themselves diminish the heat of the beds immediately 
above the melting cauldron from which they arise ; 
for the conversion of some of the fluid substances into 
gases, on the removal of the enormous pressure, will 
rapidly abstract heat from the melted mass. 

As the removal of the upper surface of the high 
land may diminish its resistance to fracture, so the 
altered pressure arising from the removal of that 
weight, and its transport to the bottom of the ocean, 
may determine the exit of the melted matter. 

Other consequences might arise from the different 
fusibility of the various strata deposited in the bed of 
the ocean. Let us imagine, in the annexed wood cut, 
the two beds, A and B, to melt at a much lower tern- 




APPENDIX. 



195 



perature than those between which they intervene. It 
might happen, by the gradual rising of the isothermal 
surfaces, that one or both of those strata should be 
melted ; and thus, supposing all the beds originally to 
have contained marine remains, we might, at a distant 
period, discover two interposed beds, having no trace 
of animal remains, but presenting all the appearances 
of former fusion, resting on, separated by, and existing 
under, other beds of demonstrably marine formation. 

If, during that state of fusion, rents should be formed 
through several of these strata, injection of the liquid 
matter might proceed both upwards and downwards 
from these melted beds. If, on the contrary, older 
dykes had penetrated all these strata, it is possible 
to suppose such circumstances of fusibility in the older 
dyke, or of its chemical relation to the melted bed, 
that the portions passing through that bed shall be 
obliterated, whilst those portions of the dyke passing 
through the less fusible beds, protected from such 
action, shall remain unaltered, as in the annexed cut. 




198 



APPENDIX. 



Another consequence of this constant change in the 
position of the isothermal surfaces must be the deve- 
lopment of thermo-electricity, which, acting on an im- 
mense scale, may determine the melting of some beds, 
or the combination of the melted masses of others, or 
cause the segregation of veins and crystals, in heated, 
but not fluid, portions of the strata exposed to its 
influence. Nor may the dykes themselves be without 
their use, either in keeping up the communication for 
the passage of electricity, if they are good conductors, 
or separating the groups of strata which produce it, 
if they are bad conductors. 

For the elucidation of this subject, it appears very 
important that experiment should be made on the 
effects of long-continued artificial heat in altering and 
obliterating the traces of organic remains existing in 
known rocks. It seems probable that we might, by a 
well-planned series of such experiments, be able to 
trace the gradually disappearing structure of animal 
remains existing in rocks subjected to fire, into marks 
which, without such aid, seem utterly remote from that 
origin ; and that we might thus establish new alpha- 
bets with which to attempt the deciphering of some 
of the older rocks. Some experiments, with this object 
in view, were undertaken at the recommendation of the 
British Association, and portions of rock, containing 
organic remains, have already been exposed, for above 
two years, to the heat of the hearth of a blast furnace, 



APPENDIX. 



197 



at the Elsecar iron works, through the permission of 
Earl Fitzwilliam, and at the Low Moor works, by that 
of the proprietors. 

It appears, therefore, that in consequence of changes 
continually going on, by the destruction of forests, the 
filling up of seas, the wearing down of elevated lands, 
the heat radiated from the earth's surface varies consi- 
derably at different periods. 

In consequence of this variation, and also in conse- 
quence of the covering up of the bottoms of seas, by 
the detritus of the land, the surfaces of equal tempera- 
ture within the earth are continually changing their 
form, and exposing thick beds near the exterior to 
alterations of temperature. The expansion and contrac- 
tion of these strata may form rents and veins, produce 
earthquakes, determine volcanic eruptions, elevate con- 
tinents, and possibly raise mountain chains. 

The consequences resulting from the working out 
of this theory would fill a volume, rather than a note. 
It may, however, be remarked, that whilst the princi- 
ples on which it is founded are really existing causes, 
yet that the sufficiency of the theory for explaining all 
the phenomena can only be admitted when it shall have 
been shown, that their power is fully equal to produce 
all the observed effects. 



198 



NOTE H. 



TABLE 



Showing the Expansion of Beds of Granite variously heated, 
from One Degree to One Hundred Degrees Fahrenheit, 
and from One to Five Hundred Miles thick. 



Miles. 


One 


Twenty 


Fifty 


One Hundred 


Degree. 


Degrees. 


Degrees. 


Degrees. 




Feet. 


Feet. 


Feet. 


Feet. 


1 


•02548 


•5095 


1-274 


2-548 


5 


•13 


2-55 


6-37 


12-74 


10 


•25 


5-10 


12-74 


25-48 


15 


•38 


7'64 


19-1 L 


38-21 


20 


•51 


10-19 


25-48 


50-95 


25 


•64 


12-74 


31-85 


63-69 


30 


•76 


15-29 


38-21 


76-43 


35 


•89 


17-83 


44-58 


89-17 


40 


1-02 


20-38 


50-95 


101-90 


45 


1-15 


22-93 


57-32 


114-64 


50 


1-27 


25-48 


63-69 


127-38 


55 


1-40 


28-02 


70-06 


140-12 


60 


1-53 


3057 


76-43 


152-86 


65 


1-66 


33-12 


82-80 


165-59 


70 


1 Jo 


d5'o7 


89 17 


I/O OO 


75 


1-91 


38-21 


95-5 


191-07 


80 


2-04 


40-76 


101-90 


203-81 


85 


2-17 


43-31 


108-27 


216-55 


90 


2-29 


45-86 


114-64 


229-28 


95 


2-42 


48-40 


121-01 


242-02 


100 


2-55 


50-95 


127*38 


254-76 


150 


382 


76-43 


191-07 


382-14 


200 


5'10 


101-90 


254-76 


509-52 


500 


12-74 


254-76 


636-90 


1273-80 



APPENDIX. 



199 



TABLE 



Showing the Expansion of Beds of Granite variously heated, 
from Tiro Hundred Degrees to Three Thousand Degrees 
Fahrenheit, and from One to Five Hundred Miles thick. 



Ames. 


Two Hundred 
Degrees. 


Five Hundred 
Degrees. 


One Thousand 
Degrees. 


Three Thousand 
Degrees. 




Feet. 


Feet. 


Feet. 


Feet. 


1 


5-095 


12-738 


25-476 


76-428 


5 


255 


63-7 


127-4 


382-1 


10 


51-0 


127'4 


254-8 


764-3 


15 


76-4 


191-1 


382-1 


1147-4 


20 


101-9 


254-8 


509-5 


1528-6 


25 


127-4 


318-5 


636 9 


1910-7 


30 


15-2-9 


382-1 


764-3 


2292-8 


35 


178-3 


445-8 


891-7 


2675-0 


40 


203-8 


509-5 


1019-0 


3057-1 


45 


229 3 


573-2 


1146-4 


3439 3 


50 


254-8 


C36-9 


1273-8 


3821-4 


55 


280-2 


700-6 


1401-2 


4203-5 


60 


305-7 


764-3 


1528-6 


4585-7 


65 


331-2 


828-0 


1655-9 


4967-S 


70 


356-7 


891-7 


1783-3 


5350-0 


75 


382-1 


955-4 


1910-7 


5732-1 


80 


407-6 


1019-0 


2038-1 


6114-2 


85 


433- 1 


1082-7 


2165-5 


6496-4 


90 


458-6 


1146-4 


2292-8 


6878-5 


95 


484-0 


1210-1 


2420-2 


7260-7 


100 


509-5 


1273-8 


2547-6 


7642-8 


150 


764-3 


1910-7 


3821-4 


11464-2 


200 


1019-0 


2547-6 


5095 2 


15285 6 


500 


2547-5 


63690 


12738 


38214 



200 



APPENDIX. 



The table was calculated from experiments made 
under the direction of Colonel Totten, by Mr. H. C. 
Bartlett, of the United States Engineers ; an account of 
which is given in the American Journal of Science, 
Vol. XXII. p. 136. 

From the result of these experiments it was found 
that, for every degree of Fahrenheit, 

Granite expands -000004825 

Marble -000005668 

Sandstone -000009532 

The tables were computed by the Calculating 
Engine, from the first line, which was deduced from 
the experiment. It will be observed that the numbers 
given are always true to the last figure, a compen- 
sation which the Engine itself made. In order to find 
the expansion for marble, increase the numbers by 
one -sixth. To find the expansion for sandstone, 
double the numbers found in the table. 

Other experiments have since been made by Mr. 
Adie, of which an account is given in the thirteenth 
volume of the Transactions of the Royal Society of 
Edinburgh : from these I have selected the following 



list of expansions : — 

Roman Cement expands -00000750 

Sicilian White Marble -00000613 

Carrara Marble -00000363 



APPENDIX. 201 

Sandstone, from Craigleith quarry .... '00000652 

Slate, from Penrhyn, Wales '00000576 

Peterhead Red Granite -00000498 

Arbroath Pavement -00000499 

Caithness Pavent -00000497 

Greenstone, from Ratho -00000449 

Aberdeen Grey Granite -00000438 

Best Stock Brick -00000306 

Fire Brick -00000274 

Black Marble, Galway -00000247 



202 



APPENDIX. 



NOTE I. 

I am happy, through the kindness of Mr. Lyell and 
Mr. Murchison, to be enabled to put before the reader 
extracts from some letters of Sir J. Herschel, which 
show, that though my early friend is extending the 
boundaries of our system, by his observations in the 
southern hemisphere, his active and indefatigable mind 
has yet found time to throw its comprehensive glance 
over some of the highest questions which perplex other 
sciences. I feel, that the almost perfect coincidence of 
his views with my own, gives additional support to the 
explanations I have offered ; whilst the reader will 
perceive, from the different light in which my friend 
has viewed the subject, that we were both independ- 
ently led to the same inferences by different courses 
of inquiry. 

" Fredhausen, Cape of Good Hope, Feb. 20, 1836. 

" My dear Sir, 
"lam perfectly ashamed not to have long since ac- 
" knowledged your present of the new edition of your 



APPENDIX. 



203 



" Geology, a work which I now read for the third 
" time, and every time with increased interest, as it 
" appears to me one of those productions which work 
" a complete revolution in their subject, by altering 
" entirely the point of view in which it must thence- 
" forward be contemplated. You have succeeded, too, 
" in adding dignity to a subject already grand, by ex- 
" posing to view the immense extent and complication 
" of the problems it offers for solution, and by unveiling 
" a dim glimpse of a region of speculation connected 
" with it, where it seems impossible to venture without 
" experiencing some degree of that mysterious awe 
" which the sybil appeals to, in the bosom of iEneas, 
" on entering the confines of the shades — or what the 
" Maid of Avenel suggests to Halbert Glendinning, 

' He that on such quest would go must know nor fear nor failing; 
To coward soul or faithless heart the search were unavailing.' 

" Of course I allude to that mystery of mysteries, the 
" replacement of extinct species by others. Many 
" will doubtless think your speculations too bold, but 
" it is as well to face the difficulty at once. For my 
" own part, I cannot but think it an inadequate con- 
" ception of the Creator, to assume it as granted that 
" his combinations are exhausted upon any one of the 
{< theatres of their former exercise, though in this, as 
" in all his other works, we are led, by all analogy, to 
M suppose that he operates through a series of inter- 
" mediate causes, and that in consequence the origina- 



204 



APPENDIX. 



" tion of fresh species, could it ever come under our 
" cognizance, would be found to be a natural in con- 
" tradistinction to a miraculous process — although we 
" perceive no indications of any process actually in 
" progress which is likely to issue in such a result." 



" Now for a bit of theory. Has it ever occurred to 
" you to speculate on the probable effect of the trans- 
" fer of pressure from one part to another of the earth's 
" surface by the degradation of existing and the for- 
" mation of new continents — on the fluid or semi -fluid 
" matter beneath the outer crust? Supposing the 
" whole to float on a sea of lava, the effect would 
" merely be an almost infinitely minute flexure of the 
" strata; but, supposing the layer next below the 
" crust to be partly solid and partly fluid, and com- 
" posed of a mixture of fixed rock, liquid lava, and 
" other masses, in various degrees of viscidity and 
" mobility, great inequalities may subsist in the dis- 
<{ tribution of pressure, and the consequence may be, 
" local disruptions of the crust, where weakest, and 
" escape to the surface of lava, &c. If the obstructions 
" to free communication among distant parts of a fluid 



APPENDIX. 



205 



" be great, no instantaneous propagation of pressure 
" can subsist, the hydrostatical law of the equality of 
" pressure being only true of fluids in a state of un- 
" disturbed equilibrium. If the whole contents of the 
" fissures, pipes, &c, into which we may consider the 
" interior divided, were lava, it is true no increase of 
" pressure on the bed of an ocean, from deposited 
" matter, could force the lava up to a higher level than 
" the surface, or so high. But if the contents be 
f( partly liquid, partly gaseous, or partly water, in a 
" state to become steam, at a diminished pressure, 
" then it may happen that the joint specific gravity of 
" lava + gas, or lava + steam occupying any given chan- 
" nel may be less than that of water ; or of the joint 
" column of water + newly deposited matter — which 
" may be brought to press upon it by any sudden giving 
" way of support, and the effect will be the escape of 
" a mixture of lava and gas, either together, as froth 
" and pumice, or by fits, according as they are disposed 
" in the channel. This (taken as a general cause of 
" volcanos) would account for the great quantity of 
u gaseous matter which always accompanies eruptions, 
" and for the final Moiv out of wind and dust with 
" which they so often terminate. It has always been 
" my greatest difficulty in Geology to find a primum 
" mobile for the volcano, taken as a general, not a 
" locnl phenomenon. Davy's speculations about the 
" oxidation of the alkaline metals seems to me a mere 
" chemical dream, and the fermentation of water and 



206 



APPENDIX. 



" pyrites as utterly insignificant on a scale of any 
" magnitude. Poulett Scrope's notion of solid rocks 
" flashing out into lava and vapour, on removal of 
"pressure, and your statement of the probable cause of 
" Volcanic Eruptions, in p. 385, vol. ii. 4th Ed. when 
ts you speak of the effect of a minute hole bored in a 
" tube, in which liquefied gases are imprisoned, both 
" appear to me wanting in explicitness, and as not going 
" high enough in the inquiry, up to its true beginning, 
" and also as giving, in some respects, a wrong notion 
6C of the process itself. The question stares us in the 
" face — How came the gases to be so condensed ? 
" Why did they submit to be urged into liquefac- 
" tion ? If they were not originally elastic, but have 
" become so by subterranean heat, whence came 
" the heat? and why did it come? How came the 
" pressure to be removed, or what caused the crack ? 
66 &c. &c. 

"It seems clear that if the gases, or aqueous vapour, 
" were once free, at so high a degree of elasticity as 
" is presumed, there exists no adequate cause for their 
" confinement, — the spring once uncoiled, there is 
e< nowhere a power capable of bending it up to the 
" pitch. We are forced therefore to admit, that the 
" elastic force has been superadded to them, during 
" their sojourn below, by an accession of temperature. 
" Now, though I cannot agree with you in your view 
" of the subject of the Central heat, p. 373, vol. ii. 4th 



APPENDIX. 



207 



" Ed. (because I see no reason why the heat may not 
" go on increasing to the very centre without necessitat- 
" ing such disturbance of equilibrium as to give rise to 
" any circulation of currents, which you there seem to 
" regard as the necessary consequence of such a state*), 
" yet I agree entirely with what you observe in p. 376, 
" — that the ordinary repose of the surface argues a 
" wonderful inertness in the interior, w T here, in fact, 
" I conceive that every thing is motionless. Under 
*' these circumstances, and debarred from that obvious 
" means of boiling our pot, the invasion of a circulat- 
" ing current, or casual injection of intensely hot 
" liquid matter from below, the question, e Whence 
"comes the heatV and ' Why did it come? remains 
" to be answered on sound theoretical grounds. Now, 
" the answer I conceive to be as follows : — 

" Granting an equilibrium of temperature and pres- 
" sure within the globe, the isothermal strata near 
" the centre will be spherical, but where (hey approach 
" the surface will, by degrees, conform themselves to 
" the configuration of the solid portion ; that is, to the 
" bottom of the sea and the surface of continents. 

* " Heated liquids circulate not because the lower parts are hotter, but 
" because they are lighter, than the upper. But in the interior of a 
" heated globe, the density depends not only on the temperature, but 
" on the pressure (i. e. the depth) of each stratum ; so that nothing is 
" easier than to imagine a law of increasing temperature which shall 
" co-exist with increasing density. 



208 



APPENDIX. 



" Suppose such a state of equilibrium, and that under 
" the bottom B of my great ocean D E, the isother- 
" mal strata are as represented by the black lines. 




" Now, let that basin be filled with solid matter up to 
" A. Immediately the equilibrium of temperature 
" will be disturbed. Why ? — because the form of a 
" stratum of temperature depends essentially on the 
" form of the bounding surface of the solid above it, 
" that form being one of the arbitrary functions which 
11 enter into its partial differential equation. Im- 
" mediately, therefore, the temperature will begin to 
" migrate from below upwards, and the isothermal 
" strata will gradually change their forms from the 
i( black to the dotted lines. The lowest portions at 
" B will then (after the lapse of ages, and when a 
" fresh state of equilibrium is attained) have acquired 
" the temperature of the stratum C, corresponding 
" to their then actual depth, while a point as deep 
" below B as C is below the surface, will have ac- 



APPENDIX. 



209 



" quired a much higher temperature, and may become 
" actually melted, and that without any bodily transfer 
" of matter in a liquid state from below. But if C be 
" already at the melting point, B will now be so — 
" i. e. the lower level will attain B, and the bottom of 
" the new strata will melt, tcater included, with which, 
" from the circumstances of the case, they must be 
" saturated. 

" Now, let the process of deposition go on, until, 
" by accumulation of pressure on the bottom or sloping 
" sides, or on some protuberance from the bottom, 
" some support gives way — a piece of the solid crust 
" breaks down, and is plunged into the liquid below, 
" and a crack takes place extending upwards. Into 
" this the liquid will rise by simple hydrostatic pres- 
" sure. But as it gains height, it is less pressed ; and 
" if it attain such a height that the ignited water can 
" become steam, the case before alluded to arises, the 
" joint specific gravity of the column is suddenly 
" diminished, and up comes a jet of mixed steam and 
" lava, till so much has escaped that the deposited 
" matter takes a fresh bearing, when the evacuation 
" ceases, and the crack becomes sealed up. 

" In the analysis I have above given of the process 
" of heating from below, we have, if I mistake not, a 
" strictly theoretical account of that great desidera- 
" turn of the Huttonian theory — 1 Let heat,' says he, 

p 



210 



APPENDIX. 



" ' invade a newly deposited stratum from below.' — 
" But why ? Not because great currents of melted 
" matter are circulating in the nucleus of the globe — 
" not because great waves of caloric are rushing to and 
" fro, without a law and without a cause in the subter- 
(( ranean regions — but simply because the fact of new 
'* strata having been deposited, alters the conditions of 
" the equilibrium of temperature, and they draw the 
" heat to them, or, which comes to the same thing, 
" retain it in them in its transit outwards (the supply 
" from the centre being supposed inexhaustible, and 
" its temperature of course invariable). 

" According to the general tenor of your book, we 
" may conclude, that the greatest transfer of material to 
" the bottom of the ocean, is produced at the coast line 
" by the action of the sea ; and that the quantity carried 
" down by rivers from the surface of continents, is 
" comparatively trifling. While, therefore, the greatest 
" local accumulation of pressure is in the central area 
" of deep seas, the greatest local relief takes place along 
" the abraded coast lines. Here, then, in this view, 
" should occur the chief volcanic vents. If the view 
" I have taken of the motionless state of the interior 
" of the earth be correct, there appears no reason why 
" any such influx of heat should take place under an 
" existing continent (say Scandinavia) as to heat incum- 
" bent rocks (whose bases retain their level) 5 or 600° 
" Fahr. for many miles in thickness, (Princ. of Geoh 



APPENDIX. 



211 



" vol. ii. p. 384. 4th Ed.) Laplace's* idea of the elevation 
" of surface due to columnar expansion (which you at- 
" tribute, in a note, to Babbage,) is in this view in- 
" adequate to explain the rise of Scandinavia, or of 
u the Andes, &c. But, in the variation of local pres- 
" sure due to the transfer of matter by the sea, on the 
<£ bed of an ocean imperfectly and unequally support- 
" ed, it seems to me an adequate cause may be found. 
" Let A be Scandinavia, B the adjacent ocean (theNorth 
" Sea), C a vast deposit, newly laid on the original bed 
" D of the ocean ; EE E a semi-fluid, or mixed 




" mass, on which D D D reposes. What will be the 
" effect of the enormous weight thus added to the bed 
" DDD (rock being heavier than sea)? Of course, 

* " Nisi Mitscherlich's. I remember well to have read it somewhere 
or other." 

[This was written before my friend had received the abstract of the 
Paper on the Temple of Scrapis, forwarded to him by Mr. Lyell. The 
reader will perceive, by Note G. of the Appendix, that isothermal sur- 
faces form the prominent feature of both our views of this question. — 
C. B.] 

p 2 



212 



APPENDIX. 



" to depress D under it, and to force it down into the 
" yielding mass E, a portion of which will be driven 
" laterally under the continent A, and upheave it. 
" Lay a weight on a surface of soft clay : you depress 
" it below, and raise it around the weight. If the 
6( surface of the clay be dry and hard, it will crack in 
" the change of figure." 



" I don't know whether I have made clear to you 
" my notions about the effects of the removal of mat- 
i( ter from above, to below, the sea. 1st. It produces 
ie a mechanical subversion of the equilibrium of pres- 
" sure. 2d\y. It also, and by a different process (as 
" above explained at large), produces a subversion of 
" the equilibrium of temperature. The last is the most 
(e important. It must be an excessively slow process, 
S( and will depend, 1st, on the depth of matter depo- 
" sited ; 2dly, on the quantity of water retained by it 
<fi under the great squeeze it has got ; 3dly, on the 
" tenacity of the incumbent mass — whether the influx 
" of caloric from below, which must take place, 
" acting on that water, shall either heave up the whole 
" mass, as a continent, or shall crack it, and escape 



I 



APPENDIX. 213 

" as a submarine volcano, or shall be suppressed 
" until the mere weight of the continually accumulat- 
" ing mass breaks its lateral supports at or near the 
" coast lines, and opens there a chain of volcanos. 

44 Thus the circuit is kept up — the primum mobile 
" is the degrading power of the sea and rains (both 
" originating in the sun's action) above, and the 
" inexhaustible supply of heat from the enormous 
" reservoirs below, always escaping at the surface, un- 
" less when repressed by an addition of fresh clothing, 
" at any particular part. In this view of the subject, 
" the tendency is outwards. Every continent deposited 
" has a propensity to rise again ; and the destructive 
*f principle is continually counterbalanced by a re-or- 
" ganizing principle from beneath. Nay, it may go 
" farther — there may be such a tendency in the globe 
" to swell into froth at its surface, as may maintain its 
" dimensions in spite of its expense of heat ; and thus 
" preserve the uniformity of its rotation on its axis, in 
" spite of the doctrines of refrigeration and contrac- 
" tion, (which, by the bye, had occurred to myself, 
" and been rejected, as inadequate to give a general 
" formula of explanation of volcanos, &c.) Perhaps 
" I shall recur to this subject on some future occa- 
" sion ; but really the stars leave me very little time 
" to lick into form any geological theories, or even 
" to examine them with any degree of scrupulous 
" severity." 



2U 



APPENDIX. 



" Feldhausen, Cape of Good Hope, Nov. 15, 1836. 

" In the letter you allude to as having been written 
" by me to Mr. Lyell, there were some speculations 
" about the effect of central heat on newly-deposited 
" matter, which, judging from some expressions in his 
" answer to that letter, I am inclined to think must 
" have been put obscurely, since he appears disposed 
<c to regard the view I took of the subject as identical 
" with some theory ascribed to Mr. Babbage (but, 1 
s( believe, before propounded by Mitscherlich) about 
" the elevation of strata by pyrometric expansiou of the 
" subjacent columns of rock, by an invasion of subter- 
" raneous heat. Granting the heat, there is no difficulty 
" in deducing expansions, disruptions, tumefactions, 
" &c. ; but this was not my drift. Will it be tres- 
" passing too much on your patience if I here state, in 
" brief, what I really had in view> — which, so far as I 
" can recollect, has not hitherto been duly, or not at 
" all, considered? If you like to call it my * theory,' 
" you may do so ; but it is not so much ' a theory,' as a 
" pursuing into its consequences, according to admitted 
" laws, of the hypothesis of a high central tempera- 
" ture, which many geologists admit, and all are fa- 
" miliar with. 

" Granting, then, as a postulate, a gradation of 
" temperature within the globe, from the observed ex- 
" ternal temperature at the surface, up to a high state 



APPENDIX. 



515 



of incandescence at the centre : I say, that when solid 
matter comes to be deposited to any considerable 
thickness on any part of the bed of the ocean, by sub- 
sidence, (or even on the surface of a continent, by 
volcanic ejection, as in great volcanic plateaux and 
table-lands, or by the action of the wind, as in sand 
hills,) the mere fact of such accession of materials, 
without requiring any other condition, or concomitant 
cause, will, of itself, in virtue of the known laws of 
the propagation of heat through a slowly-conducting 
mass, immediately subvert the equilibrium of tem- 
perature, and induce a change in the form of the 
isothermal surfaces (curves of equal temperature) in 
the whole region immediately beneath, and surround- 
ing the point of deposition — causing all those surfaces 
(which, you will observe, are only imaginary mathe- 
matical ones, like lines of equal variation in a mag- 
netic chart — not real strata) to bulge outwards, and 
1 recede from the centre in that part. The direct con- 
' sequence of this will be, that any given point of the 
' surface on which the deposit took place will, when a 
1 new state of equilibrium is attained, (supposing it to 
* be so) have a temperature corresponding to an iso- 
1 thermal surface of a deeper order: i. e., it will have 
1 become hotter than it was previous to the new de- 
1 posit ; and the same is true of every point in the 
' vertical line drawn from that point downwards. Sup- 
1 posing, as before said, a new state of equilibrium to 
1 be attained, (the deposition ceasing, by the filling up 



216 



APPENDIX. 



" of the sea in that part) then the temperature of the 
" lowest parts of the newly-formed strata will be that 
" of a point situated beneath the surface of an old con- 
" tinent in the same latitude, at a depth equal to the 
" thickness of the deposited matter. The thicker, there- 
<c fore, the deposit, the hotter will its lower portions 
" tend to grow; and, if thick enough, they may grow 
" red hot, or even melt. In the latter case, their supports 
" being also melted or softened, may wholly or partially 
" yield, under the new circumstances of pressure, to 
" which they were originally not adjusted ; and the 
" phenomena of earthquakes, volcanic explosions, &c, 
" may arrive — while, on the other hand, if no cracks 
" occur, and all goes on in quiet, the only consequence 
" will be, the obliteration of organic remains, and lines 
" of stratification, &c. — the formation of new combina- 
" tions of a chemical nature, &c. &c. — in a word, the 
" production of Lyell's c metamorphic ' rocks. 

" The process described above is precisely that by 
" which a man's skin grows warmer in a winter day by 
tf putting on an additional greatcoat; the flow of heat 
" outwards is obstructed, and the surface of congela- 
" tion carried to a distance from his person, by the 
" accumulation of heat thereby caused beneath by the 
" new covering. 

" You see, therefore, that my object is to get at a 
" geological { primum mobile, in the nature of a vera 



APPENDIX. 



217 



causa, and to trace its working in a distinct and in- 
telligible manner. In future, therefore, instead of 
saying, as heretofore, 'Let heat from below invade 
newly-deposited strata (Heaven knows how or why), 
then they will melt, expand,' &c. &c, we shall 
commence a step higher, and say, 1 Let strata be 
deposited.' Then, as a necessary consequence, and 
according to known, regular, and calculable laws, heat 
icill gradually invade them from below and around ; 
and, according to its due degree of intensity at any 
assigned time, will expand, ignite, or melt them, 
as the case may be, &c. &c. &c. ; and, I mistake 
greatly, if this be not a considerable reform in our 
geological language. 

M According to this view of the matter, there is no- 
thing casual in the formation of Metamorphic Rocks. 
All strata, once buried deep enough, (and due time 
allowed!!!) must assume that state, — none can 
escape. All records of former worlds must ulti- 
mately perish. 

" P.S. — If you think it worth while to read the above 
1 speculation whenever a discussion may arise, natu- 
1 rally leading to it, at any meeting of the Geological 
c Society, (not as a formal communication, for I have 
£ not time to put it into shape, or work it out in detail, 
1 but incidentally) you are quite at liberty to do so ; 
' and I shall be glad to know your own opinion of it." 



218 



APPENDIX. 



NOTE K. 

ON THE ELEVATION OF BEACHES BY TIDES. 

If the earth were a spheroid of revolution, covered 
by one uniform ocean, two great tidal waves would 
follow each other round the globe at a distance of twelve 
hours. 

Suppose several high narrow strips of land were now 
to encircle the globe, passing through the opposite 
poles, and dividing the earth's surface into several great 
unequal oceans, a separate tide would be raised in each. 
When the tidal wave had reached the farthest shore of 
one of them, conceive the causes that produce it to 
cease ; then the wave thus raised would recede to the 
opposite shore, and continue to oscillate until destroyed 
by the friction of its bed. But if, instead of ceasing 
to act, the causes which produced the tide were to 



APPENDIX. 



219 



reappear at the opposite shore of the ocean, at the very 
moment when the reflected tide had returned to the 
place of its origin ; then the second tide would act in 
augmentation of the first, and, if this continued, tides 
of great height might be produced for ages. The 
result might be, that the narrow ridge dividing the 
adjacent oceans would be broken through, and the 
tidal wave traverse a broader tract than in the former 
ocean. Let us imagine the new ocean to be just 
so much broader than the old, that the reflected tide 
would return to the origin of the tidal movement half 
a tide later than before : then, instead of two super- 
imposed tides, we should have a tide arising from the 
subtraction of one from the other. The alterations 
of the height of the tides on shores so circumstanced, 
might be very small j and this might again continue for 
ages : thus causing beaches to be raised at very differ- 
ent elevations, without any real alteration in the level 
either of the sea or land. 

If we consider the superposition of derivative tides, 
similar effects might be found to result ; and it deserves 
inquiry, whether it may not be possible to account for 
some remarkable and well-attested phenomena by such 
means. 

The gradual elevation during the past century, of 
one portion of the Swedish coast above the Baltic, 
is a recognised fact, and has lately been verified by 



220 



APPENDIX. 



Mr. LyelL* It is not probable, from the form and posi- 
tion of that sea, that two tides should reach it distant 
by exactly half the interval of a tide, and thus produce 
a very small tide ; nor is it likely that by the gradual 
but slow erosion of the longer channel, one tide 
should almost imperceptibly advance upon the other : 
but it becomes an interesting question to examine whe- 
ther, in other places, under such peculiar circumstances, 
it might not be possible that a series of observations of 
the heights of tides at two distant periods, might give 
a different position for the mean level of the sea at 
places so situated. 

If we conceive two tides to meet at any point, one of 
which is twelve hours later than the other, the eleva- 
tion of the waters will arise from the joint influence of 
both. Let us suppose, that from the abrasion of the 
channel, the later tide arrives each time one-hundredth 
of a second earlier than before. After about 3,150 
years, the high water of the earlier tide will coincide in 
point of time with the low water of the later tide : and 
the difference of height between high and low water 
will be equal to the difference of the height of the two 
tides, instead of to their sum, as it was at the first 
epoch. 

If, in such circumstances, the two tides were nearly 



* See Phil. Trans. 1836. 



APPENDIX. 



equal in magnitude, it might happen that on a coast so 
circumstanced, there would at one time be scarcely 
any perceptible tide ; and yet, 3000 years after, the 
tide might rise 30 or 40 feet, or even higher; and this 
would happen without any change of relative height in 
the land and water during the intervening time. Pos- 
sibly this view of the effects which may arise, either 
from the wearing down of channels, or the filling up of 
seas through which tides pass, may be applied to ex- 
plain some of the phenomena of raised beaches, which 
are of frequent occurrence. 

Natural philosophers are at present not quite agreed 
upon the mode of determining the mean level of the 
ocean. Whether it is to be deduced from the averages 
between the highest and lowest spring tide, or from the 
averages of all the intermediate ones, or from the means 
of the instantaneous heights of the tide at all interven- 
ing periods — or by whatever other process, its true 
level is yet to be ascertained. It may, perhaps, also 
be useful to suggest that, besides the actual level of 
the sea at any particular place, it would be also desir- 
able to ascertain whether the time of high water at 
given epochs is not itself a changeable quantity. 

These reflections, however, are only thrown out with 
the view of exciting discussion on a subject involved at 
present in great mathematical difficulties, and possess- 
ing, at the same time, the highest practical importance. 



222 



APPENDTX. 



NOTE L. 

ON RIPPLE-MARK. 

The small waves raised on the surface of the water, 
by the passage of a slight breeze, are called Ripple ; 
and a series of marks, very similar in appearance, 
which are sometimes seen at low water on the flat 
part of a sea-beach formed of fine sand, are called 
ripple-marks. Such marks occur in various strata, 
and are regarded as evidence of their having formed 
beneath the sea. Similar appearances occur when a 
strong wind drives over the face of a sandy plain. 

It appears that two fluids of different specific gravity, 
the lighter passing over the surface of the former, al- 
ways concur in the formation of ripple. It seems also, 
that the lines of ripple-mark are at right angles to the 
direction of the current which forms them. 



APPENDIX. 



223 



If a fluid like air pass over the surface of perfectly 
quiescent water, in a plain absolutely parallel, it will 
have no effect ; but if it impinge on the surface of that 
water with the slightest inclination, it will raise a small 
wave, which will be propagated by undulations to great 
distances. If the direction of the wind is very nearly 
parallel to the surface of the water, this first wave, being 
raised above the general surface, will protect that part 
of the water immediately beyond it from the full effect 
of the wind, which will therefore again impinge upon 
the water at a little distance : and, this concurring with 
the undulation, will tend to produce another small 
wave, and thus, again, new waves will be produced. 
But the under surface of the air itself will also assume 
the form of waves, and so, on the slightest deviation 
at any one point from absolute parallelism in the two 
fluids, their whole surfaces will become covered with 
ripples. 

If one of the fluids be water, and the lower fluid be 
fine sand, partially supported in water, these marks 
do not disappear when the cause ceases to act, as they 
do when formed by air on the surface of water. These 
are the marks we observe when the tide has receded 
from a flat, sandy shore. 

If, after the formation of ripple-marks at the bottom 
of a shallow sea, some adjacent river or some current 
deposit upon them the mud which it holds in suspension, 



224 



APPENDIX. 



then the former marks will be preserved, and new ripple 
marks may appear above them. Such is the origin of 
those marks we observe in various sand-stones, from the 
most recent down to those of the coal measures. 

Dr. Fitton informs me, that he found the sand hills 
on the south of Etaples (in France) consisting of ripple- 
marks on a large scale. They are crescent-shaped 
hillocks, many of which are more than a hundred feet 
high. The height is greatest in the middle of the 
crescents, declining towards the points ; and the slope 
on the inner side of the crescent, which is remote from 
the prevailing direction of the winds, is much more 
rapid than that on which it strikes. 

Mr. Lyell has observed and described this mode 
of formation of ripple on the dunes of sand near 
Calais; remarking, that in that case there is an actual 
lateral transfer ; the grains of sand being carried by the 
wind up the less inclined slope of the ripple, and fall- 
ing over the steep scarp. I have observed the same 
fact at Swansea. 

A similar explanation seems to present itself as the 
origin of that form of clouds familiarly known as " a 
mackarel sky" — a wave-like appearance, which pro- 
bably arises from the passage of a current of air above 
or below a thin stratum of clouds. The air, being of 
nearly the same specific gravity as that of the cloud it 



APPENDIX 



225 



acts upon, would produce ripple of larger size than 
would otherwise occur. 

The surface of the sun presents to very good tele- 
scopes a certain mottled appearance, which is not 
exactly ripple, and which it is difficult to convey by 
description. It may, however, be suggested, that 
wherever such appearances occur, whether in planetary 
or in stellar bodies, or in the minuter precincts of the 
dye-house and the engine-boiler, they indicate the 
fitness of an inquiry, whether there are not two cur- 
rents of fluid or semi-fluid matter, one moving with a 
different velocity over the other, the direction of the 
motion being at right angles to the lines of waves. 



Q 



226 



APPENDIX. 



NOTE M. 

ON THE AGE OF STRATA, AS INFERRED FROM THE 
RINGS OF TREES EMBEDDED OF THEM. 

The indelible records of past events which are pre- 
served within the solid substance of our globe, may be 
in some measure understood without that refined ana- 
lysis on which their complete knowledge depends. 
The remains of vegetation, and of animal life, em- 
bedded in their coeval rocks, attest the existence of other 
times ; and as science and the arts advance, we shall 
be enabled to read the minuter details of their living 
history. The object of the present note is to suggest 
to the reader a line of inquiry, by which we may still 
trace some small portion of the history of the past in 
the fossil woods which occur in so many of our strata. 

It is well known that dicotyledonous trees increase 
in size by the deposition of an additional layer annually 



APPENDIX. 



227 



between the wood and the bark, and that a transverse 
section of such trees presents the appearance of a series 
of nearly concentric irregular rings, the number of 
which indicates the age of the tree. The relative 
thickness of these rings depends on the more or less 
flourishing state of the plant during the years in which 
they were formed. Each ring may, in some trees, be 
observed to be subdivided into others, thus indicating 
successive periods of the same year during which its 
vegetation was advanced or checked. These rings are 
disturbed in certain parts by irregularities resulting 
from branches ; and the year in which each branch first 
sprung from the parent stock may be ascertained by 
proper sections. 

It has been found by experiment, that even the 
motion imparted to a tree by the winds has an influ- 
ence on its growth. Two young trees of equal size 
and vigour were selected and planted in similar circum- 
stances, except that one was restrained from having 
any motion in the direction of the meridian, by two 
strong ropes fixed to it, and connecting it to the ground, 
at some distance to the north and south. The other 
tree was by similar means prevented from having any 
motion in the direction of east and west. After several 
years, both trees were cut down, and the sections of 
their stems were found to be oval; but the longer axis 
of the oval of each was in the direction in which it had 
been capable of being moved by the winds. 

Q 2 



228 



APPENDIX. 



These prominent effects are obvious to our senses; 
but every shower that falls, every change of tempe- 
rature that occurs, and every wind that blows, leaves on 
the vegetable world the traces of its passage ; slight, 
indeed, and imperceptible, perhaps, to us, but not the 
less permanently recorded in the depths of those 
woody fabrics. 

All these indications of the growth of the living 
tree are preserved in the fossil trunk, and with them 
also frequently the history of its partial decay. Let 
us now examine the use we may make of these details 
relative to individual trees, when considering forests 
submerged by seas, embedded in peat mosses, or 
transformed, as in some of the harder strata, into stone. 
Let us imagine, that we possessed sections of the 
trunks of a considerable number of trees, such as those 
occurring in the bed called the Dirt-bed,* in the island 
of Portland. If we were to select a number of trees 
of about the same size, we should probably find many 
of them to have been contemporaries. This fact would 
be rendered probable if we observed, as we doubtless 
should do, on examining the annual rings, that some 
of them conspicuous for their size occurred at the same 
distances of years in several trees. If, for example, we 

* The reader will find an account of these fossil trees, and the strata 
in which they occur, in several papers by Dr. Buckland, Mr. De la 
Beche, and Dr. Fitton, in the Transactions of the Geological Society 
of London, vol. iv. Series 2. ' 



APPENDIX. 



found on several trees a remarkably large annual ring, 
followed at the distance of seven years by a remarkably 
thin ring, and this again, after two years , followed by 
another large ring, we should reasonably infer from these 
trees, that seven years after a season highly favourable to 
their growth, there had occurred a season peculiarly 
unfavourable to them: and that after two more years 
another very favourable season had happened, and that 
all the trees so observed had existed at the same period 
of time. The nature of the season, whether hot or 
cold, wet or dry, would be known with some degree of 
probability, from the class of tree under consideration. 
This kind of evidence, though slight at first, receives 
additional and great confirmation by the discovery of 
every new ring which supports it; and, by a consider- 
able concurrence of such observations, the succession 
of seasons might be in some measure ascertained at 
remote geological periods. 

On examining the shape of the sections of such 
trees, we might perceive some general tendency to- 
wards a uniform inequality in their diameters ; and we 
might perhaps observe that the longer axes of the 
sections most frequently pointed in one direction. If 
we knew from the species of tree that it possessed no 
natural tendency to such an inequality, then we might 
infer that, during the growth of these trees, they were 
bent most frequently in one direction ; and hence an 
indication of the prevailing winds at that time. In 



230 



APPENDIX. 



order to find from which of the two opposite quarters 
these winds came, we might observe the centres of 
these sections ; and we should generally find that the 
rings on one side were closer and more compressed 
than those on the opposite side. From this we might 
infer the most exposed side, or that from which the 
wind most frequently blew. Doubtless there would 
be many exceptions arising from local circumstances — 
some trees might have been sheltered from the direct 
course of the wind, and have only been acted upon by an 
eddy. Some might have been protected by an adjacent 
large tree, sufficiently near to shelter it from the ruder 
gales, but not close enough to obstruct the light and 
air by which it was nourished. Such a tree might have 
a series of large and rather uniform rings, during the 
period of its protection by its neighbour; and these 
might be followed by a series of stinted and irregular 
ones, occasioned by the destruction of its protector. 
The same storm might have mutilated some trees, and 
half-uprooted others : these latter might strive to sup- 
port themselves for years, making but little addition, by 
stinted layers, to the thickness of their stems; and then, 
having thrown out new roots, they might regain their 
former rate of growth, until a new tempest again 
shook them from their places. Similar effects might 
result from floods and the action of rivers on the 
trees adjacent to their banks. But all these local 
and peculiar circumstances would disappear, if a 
sufficient number of sections could be procured from 



APPENDIX. 



231 



fossil trees, spread over a considerable extent of 
country. 

Similar rings might however furnish other inti- 
mations of a successive existence of these trees. 

On examining some rings remarkable for their size 
and position, we might find, for instance, in one sec- 
tion, two remarkably large rings, separated from 
another large ring, by one very stinted ring, and this 
followed, after three ordinary years, by two very small 
and two very large rings. Such a group might be 
indicated by the letters — 

oLLsooosLLoo 
where o denotes an ordinary year, or ring, L a large 
one, and s a small or stinted ring. 

If such a group occurred in the sections of several 
different trees, it might fairly be attributed to general 
causes. 

Let us now suppose such a group to be found near 
the centre of one tree, and towards the external edge 
or bark of another; we should certainly conclude, 
that the tree near whose bark it occurred was the more 
ancient tree ; that it had been advanced in age when 
that group of seasons occurred which had left their 
mark near the pith of the more recent tree, which 
was young at the time those seasons happened. If, 



232 



APPENDIX. 



on counting the rings of this tree, we found that there 
were, counting inward from the bark to this remark- 
able group, three hundred and fifty rings, we should 
justly conclude that, three hundred and fifty years 
before the death of this tree, which we will call A, 
the other, which we will call B, and whose section we 
possess, had then been an old tree. If we now search 
towards the centre of the second tree B, for another 
remarkable group of rings ; and if we also find a similar 
group near the bark of a third tree, which we will call 
C; and if, on counting the distance of the second 
group from the first in B, we find an interval of 420 
rings, then we draw the inference that the tree A, 350 
years before its destruction, was influenced in its 
growth by a succession of ten remarkable seasons, 
which also had their effect on a neighbouring tree B, 
which was at that time of a considerable age. We 
conclude further, that the tree B was influenced in its 
youth, or 420 years before the group of the ten seasons, 
by another remarkable succession of seasons, which also 
acted on a third tree, C, then old. Thus we connect 
the time of the death of the tree A with the series of 
seasons which affected the tree C in its old age, at a 
period 770 years antecedent. If we could discover 
other trees having other cycles of seasons, capable of 
identification, we might trace back the history of that 
ancient forest, and possibly find in it some indications 
for conjecturing the time occupied in forming the stratum 
in which it is embedded. 



APPENDIX. 



233 



The application of these views to ascertaining the 
age of submerged forests, or to that of peat mosses, 
may possibly connect them ultimately with the chrono- 
logy of man. Already we have an instance of a wooden 
hut with a stone hearth before it, and burnt wood on 
it, and a gate leading to a pile of wood, discovered at 
a depth of fifteen feet below the surface of a bog in 
Ireland : and it was found that this hut had probably 
been built when the bog had only reached half its 
present thickness, since there were still fifteen feet of 
turf below it. 

The realization of the views here thrown out will 
require the united exertions of many individuals pa- 
tiently exerted through a series of years. The first 
step must be to study fully the relations of the annual 
rings in every part of an individual tree. The effect 
of a favourable or unfavourable season on a section 
near the root must be compared with the influence of 
the same circumstance on its growth towards the top of 
the tree. Vertical sections also must be examined in 
order to register the annual additions to its height, and 
to compare them with its increase of thickness. Every 
branch must be traced to its origin, and its sections 
be registered. The means of identifying the influence 
of different seasons in various sections of the same indi- 
vidual tree and its branches being thus attained, the 
conclusions thus arrived at must be applied to several 
trees under similar circumstances, and such modi Hon- 



234 



APPENDIX. 



tions must be applied to them as the case may require ; 
and before any general conclusions can be reached re- 
specting a tract of country once occupied by a forest, 
it will be necessary to have a considerable number of 
sections of trees scattered over various parts of it. 



APPENDIX. 



235 



NOTE N. 

ON A METHOD OF MULTIPLYING ILLUSTRATIONS 
FROM WOOD-CUTS. 

Finding the number of wood-cuts necessary to 
explain the parts of the Calculating Engine consider- 
able, and the expense great, it appeared to me that 
the method of copying by casting might, perhaps, be 
employed for the purpose of diminishing the evil. 

The plan which occurred to me was, to make a 
drawing of that portion of the mechanism required to 
be explained, which should contain every part neces- 
sary for its action, and, in some cases, even the frame- 
work requisite for its support. Such a drawing would 
be far too complicated for the ordinary reader, and 
might appear confusion even to the contriver of the 
machine. This drawing was then to be sent to the 
wood-cutter to be engraved, and on its return, it was to 
be sent to the stereotype founder, for the purpose of 



236 



APPENDIX. 



having any number of fac-similes made in type-metal. 
Now, each of these plates would, like the original 
wood-cut, express the drawing in relief, and, by cut- 
ting away any line in the plate, that line would be re- 
moved in the impression. 

The first thing to be done was, to remove from one 
of these stereotype plates every line, except those which 
formed the framing of the mechanism. The next step 
was, to remove from another of those plates all the 
framing, and every other line, except those which re- 
presented two or three of the principal wheels and 
levers. 

If there should be many such parts, several plates 
might be taken, on each of which some few parts, not 
interfering with each other, might be allowed to re- 
main. Other plates might then be taken, on which 
the parts given on two or more of the former plates, 
might be allowed to remain, and other plates might 
again contain combinations of three or more of these. 
Thus, by a series of plates, commencing with the sim- 
plest portions of the mechanism, we might gradually 
advance through the various combinations, up to the 
original wood-cut, which, by means of such steps, 
might be made perfectly intelligible. 

The original wood-cut will be more expensive, on 
account of the additional work contained in it ; but its 



APPENDIX. 



multiplication by casting is a cheap process; and the 
cutting away some of the lines of each plate, and 
dotting others, by removing small portions at short 
intervals, which might, in different plates, require to be 
represented as passing behind other lines, is not a 
work of much difficulty or expense. The quantity of 
illustrations, all printed with the letter-press, which 
this plan admits of, renders it possible to explain much 
more complicated machinery than could be accom- 
plished by engraving, unless at an expense which 
would effectually preclude its application ; whilst the 
successive picture of every wheel and lever, exhibited 
on separate plates if necessary, as well as of every 
one of those binary and other combinations which are 
employed, will render the machinery intelligible to 
a much larger class of persons than those who usually 
study such subjects. 

The same principle may be applied to coloured 
geological sections and maps. The whole drawing 
having been sent to the wood-cutter, as many stereo- 
type fac-similes may be made from his block as there 
are colours to be represented. One plate may then be 
taken, from which all the parts are to be scraped out 
which are not to be coloured brown ; another may be 
taken from which all parts not to be coloured green ; 
and so on for all the rest of the colours. The perfect 
identity of the plates will render it easy to preserve 
what is technically termed the register, that is, to 



238 



APPENDIX. 



prevent the overlapping of any one colour on any 
other. 

As the method here suggested is extremely simple 
in its means, it is scarcely possible but that it must 
have occurred to others ; and it may, perhaps — al- 
though I am not aware of it — have been employed on 
some occasions. I have, however, thought, that in 
giving publicity to it, I should be doing a service to 
those whose writings require pictorial illustration, and 
especially to those who cultivate the sciences of me- 
chanics and geology. Perhaps, also, the same system 
might be applied to multiply, at a cheap rate, the 
blocks used in colour printing, both upon paper and 
on woven fabrics. 

On the opposite page, the reader will find an illus- 
tration of this art ; it is the same plate as that at page 
190: it is not very favourable either as to the degree 
of difficulty, or as to the question of economy ; but it 
is the only one that the subject of this volume ad- 
mitted, and is quite sufficient to explain the principle. 

The figure at the bottom of the page, No. 4, is the 
impression from a stereotype plate, which is a fac- 
simile from the original wood-cut, engraved for the 
illustration. No. 3, the next above, is the impression 
from another stereotype plate, from which the lines 
marked D and F, on No. 4, have been cut away. 



No. 1. 




No. 2. 




No. 3. 



— c 



No. 4. 



240 



APPENDIX. 



No. 2 is the impression from another plate from which 
the line E has been cut away ; and No. 1 is an im- 
pression from a similar plate, from which the lines C 
and E have been cut out. 

The four individual plates have been soldered toge- 
ther, and form the stereotype plate of the page re- 
ferred to. 



THE END. 



R. CLAY, PRINTER, BREAD-STREET-HILL. 



